0.02t if 0 t 3 δ t = if 3 < t


 Diana O’Connor’
 3 years ago
 Views:
Transcription
1 1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve dscount rate of d. The amount of nterest earned n Bruce s account durng the 11th year s equal to X. The amount of nterest earned n Robbe s account durng the 17th year s also equal to X. Calculate X. (A) 28.0 (B) 31.3 (C) 34.6 (D) 36.7 (E) (# 12, May 2003). Erc deposts X nto a savngs account at tme 0, whch pays nterest at a nomnal rate of, compounded semannually. Mke deposts 2X nto a dfferent savngs account at tme 0, whch pays smple nterest at an annual rate of. Erc and Mke earn the same amount of nterest durng the last 6 months of the 8th year. Calculate. (A) 9.06% (B) 9.26% (C) 9.46% (D) 9.66% (E) 9.86% 3. (# 50, May 2003). Jeff deposts 10 nto a fund today and 20 ffteen years later. Interest s credted at a nomnal dscount rate of d compounded quarterly for the frst 10 years, and at a nomnal nterest rate of 6% compounded semannually thereafter. The accumulated balance n the fund at the end of 30 years s 100. Calculate d. (A) 4.33% (B) 4.43% (C) 4.53% (D) 4.63% (E) (#25 Sample Test). Bran and Jennfer each take out a loan of X. Jennfer wll repay her loan by makng one payment of 800 at the end of year 10. Bran wll repay hs loan by makng one payment of 1120 at the end of year 10. The nomnal semannual rate beng charged to Jennfer s exactly one half the nomnal sem annual rate beng charged to Bran. Calculate X. A. 562 B. 565 C. 568 D. 571 E (#1 May 2003). Bruce deposts 100 nto a bank account. Hs account s credted nterest at a nomnal rate of nterest convertble semannually. At the same tme, Peter deposts 100 nto a separate account. Peter s account s credted nterest at a force of nterest of δ. After 7.25 years, the value of each account s 200. Calculate ( δ). (A) 0.12% (B) 0.23% (C) 0.31% (D) 0.39% (E) 0.47% 6. (#23, Sample Test). At tme 0, deposts of 10, 000 are made nto each of Fund X and Fund Y. Fund X accumulates at an annual effectve nterest rate of 5 %. Fund Y accumulates at a smple nterest rate of 8 %. At tme t, the forces of nterest on the two funds are equal. At tme t, the accumulated value of Fund Y s greater than the accumulated value of Fund X by Z. Determne Z. A B C D E
2 7. (#24, Sample Test). At a force of nterest δ t = 2 k+2t. () a depost of 75 at tme t = 0 wll accumulate to X at tme t = 3; and () the present value at tme t = 3 of a depost of 150 at tme t = 5 s also equal to X. Calculate X. A. 105 B. 110 C. 115 D. 120 E (# 37, May 2000). A customer s offered an nvestment where nterest s calculated accordng to the followng force of nterest: 0.02t f 0 t 3 δ t = f 3 < t The customer nvests 1000 at tme t = 0. What nomnal rate of nterest, compounded quarterly, s earned over the frst four year perod? (A) 3.4% (B) 3.7% (C) 4.0% (D) 4.2% (E) 4.5% 9. (# 53, November 2000). At tme 0, K s deposted nto Fund X, whch accumulates at a force of nterest δ t = 0.006t 2. At tme m, 2K s deposted nto Fund Y, whch accumulates at an annual effectve nterest rate of 10%. At tme n, where n > m, the accumulated value of each fund s 4K. Determne m. (A) 1.6 (B) 2.4 (C) 3.8 (D) 5.0 (E) (# 45, May 2001). At tme t = 0, 1 s deposted nto each of Fund X and Fund Y. Fund X accumulates at a force of nterest δ t = t2. Fund Y accumulates at a nomnal rate of k dscount of 8% per annum convertble semannually. At tme t = 5, the accumulated value of Fund X equals the accumulated value of Fund Y. Determne k. (A) 100 (B) 102 (C) 104 (D) 106 (E) (# 49, May 2001). Tawny makes a depost nto a bank account whch credts nterest at a nomnal nterest rate of 10% per annum, convertble semannually. At the same tme, Fabo deposts 1000 nto a dfferent bank account, whch s credted wth smple nterest. At the end of 5 years, the forces of nterest on the two accounts are equal, and Fabo s account has accumulated to Z. Determne Z. (A) 1792 (B) 1953 (C) 2092 (D) 2153 (E) (# 1, May 2000). Joe deposts 10 today and another 30 n fve years nto a fund payng smple nterest of 11% per year. Tna wll make the same two deposts, but the 10 wll be deposted n years from today and the 30 wll be deposted 2n years from today. Tna s deposts earn an annual effectve rate of 9.15%. At the end of 10 years, the accumulated 2
3 amount of Tna s deposts equals the accumulated amount of Joe s deposts. Calculate n. (A) 2.0 (B) 2.3 (C) 2.6 (D) 2.9 (E) (# 1, November 2001 ). Erne makes deposts of 100 at tme 0, and X at tme 3. The fund grows at a force of nterest δ t = t2, t > 0. The amount of nterest earned from tme 3 to 100 tme 6 s X. Calculate X. (A) 385 (B) 485 (C) 585 (D) 685 (E) (# 24, November 2001). Davd can receve one of the followng two payment streams: () 100 at tme 0, 200 at tme n, and 300 at tme 2n () 600 at tme 10 At an annual effectve nterest rate of, the present values of the two streams are equal. Gven ν n = , determne. (A) 3.5% (B) 4.0% (C) 4.5% (D) 5.0% (E) 5.5% 15. (# 17, May 2003). An assocaton had a fund balance of 75 on January 1 and 60 on December 31. At the end of every month durng the year, the assocaton deposted 10 from membershp fees. There were wthdrawals of 5 on February 28, 25 on June 30, 80 on October 15, and 35 on October 31. Calculate the dollar weghted rate of return for the year. (A) 9.0% (B) 9.5% (C) 10.0% (D) 10.5% (E) 11.0% 16. (#32, Sample Test). 100 s deposted nto an nvestment account on January 1, You are gven the followng nformaton on nvestment actvty that takes place durng the year: Aprl 19, 1998 October 30, 1998 Value mmedately pror to depost Depost 2X X The amount n the account on January 1, 1999 s 115. Durng 1998, the dollar weghted return s 0% and the tmeweghted return s y. Calculate y. (A) 1.5% (B) 0.7% (C) 0.0% (D) 0.7% (E) 1.5% 17. (# 27, November 2000). An nvestor deposts 50 n an nvestment account on January 1. The followng summarzes the actvty n the account durng the year: Date Value Immedately Before Depost Depost March June October
4 On June 30, the value of the account s On December 31, the value of the account s X. Usng the tme weghted method, the equvalent annual effectve yeld durng the frst 6 months s equal to the (tmeweghted) annual effectve yeld durng the entre 1year perod. Calculate X. (A) (B) (C) (D) (E) (#31, May 2001). You are gven the followng nformaton about an nvestment account: Date Value Immedately Before Depost Depost January 1 10 July 1 12 X December 31 X Over the year, the tme weghted return s 0%, and the dollarweghted return s Y. Calculate Y. (A) 25% (B) 10% (C) 0% (D) 10% (E) 25% 19. (#16, May 2000 ). On January 1, 1997, an nvestment account s worth 100, 000. On Aprl 1, 1997, the value has ncreased to 103,000 and 8, 000 s wthdrawn. On January 1, 1999, the account s worth 103, 992. Assumng a dollar weghted method for 1997 and a tme weghted method for 1998, the annual effectve nterest rate was equal to x for both 1997 and Calculate x. (A) 6.00% (B) 6.25% (C) 6.50% (D) 6.75% (E) 7.00% 20. (# 28, November 2001). Payments are made to an account at a contnuous rate of (8k+tk), where 0 t 10. Interest s credted at a force of nterest δ t = 1. After 10 years, the 8+t account s worth 20, 000. Calculate k. (A) 111 (B) 116 (C) 121 (D) 126 (E) (# 2, November, 2000) The followng table shows the annual effectve nterest rates beng credted by an nvestment account, by calendar year of nvestment. The nvestment year method s applcable for the frst 3 years, after whch a portfolo rate s used: Calendar year calendar of orgnal year of Portfolo nvestment Portfolo rate Rate % 10% t% % % 5% 10% 1994 t 1% % t 2% 12% % % 11% 6% % % 7% 10% % 4
5 An nvestment of 100 s made at the begnnng of years 1990, 1991, and The total amount of nterest credted by the fund durng the year 1993 s equal to Calculate t. (A) 7.00 (B) 7.25 (C) 7.50 (D) 7.75 (E) (# 51, November, 2000) An nvestor deposts 1000 on January 1 of year x and deposts another 1000 on January 1 of year x+2 nto a fund that matures on January 1 of year x+4. The nterest rate on the fund dffers every year and s equal to the annual effectve rate of growth of the gross domestc product (GDP) durng the 4 th quarter of the prevous year. The followng are the relevant GDP values for the past 4 years: Year III Quarter IV Quarter Year Quarter III Quarter III x x x x What s the nternal rate of return earned by the nvestor over the 4 year perod? (A) 1.66% (B) 5.10% (C) 6.15% (D) 6.60% (E) 6.78% 23. (#26, Sample Test). Carol and John shared equally n an nhertance. Usng hs nhertance, John mmedately bought a 10year annutydue wth an annual payment of 2500 each. Carol put her nhertance n an nvestment fund earnng an annual effectve nterest rate of 9%. Two years later, Carol bought a 15year annutymmedate wth annual payment of Z. The present value of both annutes was determned usng an annual effectve nterest rate of 8%. Calculate Z. A B C D E (#27, Sample Test). Susan and Jeff each make deposts of 100 at the end of each year for 40 years. Startng at the end of the 41st year, Susan makes annual wthdrawals of X for 15 years and Jeff makes annual wthdrawals of Y for 15 years. Both funds have a balance of 0 after the last wthdrawal. Susan s fund earns an annual effectve nterest rate of 8 %. Jeff s fund earns an annual effectve nterest rate of 10 %. Calculate Y X. A B C D E (# 22, November 2000). Jerry wll make deposts of 450 at the end of each quarter for 10 years. At the end of 15 years, Jerry wll use the fund to make annual payments of Y at the begnnng of each year for 4 years, after whch the fund s exhausted. The annual effectve rate of nterest s 7%. Determne Y. (A) 9573 (B) 9673 (C) 9773 (D) 9873 (E)
6 26. (# 27, November 2001). A man turns 40 today and wshes to provde supplemental retrement ncome of 3000 at the begnnng of each month startng on hs 65th brthday. Startng today, he makes monthly contrbutons of X to a fund for 25 years. The fund earns a nomnal rate of 8% compounded monthly. Each 1000 wll provde for 9.65 of ncome at the begnnng of each month startng on hs 65th brthday untl the end of hs lfe. Calculate X. (A) (B) (C) (D) (E) (# 47, May 2000). Jm began savng money for hs retrement by makng monthly deposts of 200 nto a fund earnng 6% nterest compounded monthly. The frst depost occurred on January 1, Jm became unemployed and mssed makng deposts 60 through 72. He then contnued makng monthly deposts of 200. How much dd Jm accumulate n hs fund on December 31, 1999? (A) 53, 572 (B) 53, 715 (C) 53, 840 (D) 53, 966 (E) 54, (# 12, November 2001). To accumulate 8000 at the end of 3n years, deposts of 98 are made at the end of each of the frst n years and 196 at the end of each of the next 2n years. The annual effectve rate of nterest s. You are gven (l + ) n = 2.0. Determne. (A) 11.25% (B) 11.75% (C) 12.25% (D) 12.75% (E) 13.25% 29. (# 34, November 2000). Chuck needs to purchase an tem n 10 years. The tem costs 200 today, but ts prce nflates 4% per year. To fnance the purchase, Chuck deposts 20 nto an account at the begnnng of each year for 6 years. He deposts an addtonal X at the begnnng of years 4, 5, and 6 to meet hs goal. The annual effectve nterest rate s 10%. Calculate X. (A) 7.4 (B) 7.9 (C) 8.4 (D) 8.9 (E) (# 8, May 2003). Kathryn deposts 100 nto an account at the begnnng of each 4 year perod for 40 years. The account credts nterest at an annual effectve nterest rate of. The accumulated amount n the account at the end of 40 years s X, whch s 5 tmes the accumulated amount n the account at the end of 20 years. Calculate X. (A) 4695 (B) 5070 (C) 5445 (D) 5820 (E) (# 33, May 2003). At an annual effectve nterest rate of, > 0, both of the followng annutes have a present value of X: () a 20 year annuty mmedate wth annual payments of 55 () a 30 year annuty mmedate wth annual payments that pays 30 per year for the frst 10 years, 60 per year for the second 10 years, and 90 per year for the fnal 10 years Calculate X. (A) 575 (B) 585 (C) 595 (D) 605 (E) 615 6
7 32. (# 17, May 2001). At an annual effectve nterest rate of, > 0%, the present value of a perpetuty payng 10 at the end of each 3 year perod, wth the frst payment at the end of year 6, s 32. At the same annual effectve rate of, the present value of a perpetuty mmedate payng 1 at the end of each 4month perod s X. Calculate X. (A) 38.8 (B) 39.8 (C) 40.8 (D) 41.8 (E) (# 5, May 2001). A perpetuty mmedate pays X per year. Bran receves the frst n payments, Colleen receves the next n payments, and Jeff receves the remanng payments. Bran s share of the present value of the orgnal perpetuty s 40%, and Jeff s share s K. Calculate K. (A) 24% (B) 28% (C) 32% (D) 36% (E) 40% 34. (# 50, May 2001). The present values of the followng three annutes are equal: () perpetuty mmedate payng 1 each year, calculated at an annual effectve nterest rate of 7.25% () 50 year annutymmedate payng 1 each year, calculated at an annual effectve nterest rate of j% () n year annutymmedate payng 1 each year, calculated at an annual effectve nterest rate of j 1% Calculate n. (A) 30 (B) 33 (C) 36 (D) 39 (E) (# 14, May 2000). A perpetuty payng 1 at the begnnng of each 6 month perod has a present value of 20. A second perpetuty pays X at the begnnng of every 2 years. Assumng the same annual effectve nterest rate, the two present values are equal. Determne X. (A) 3.5 (B) 3.6 (C) 3.7 (D) 3.8 (E) (#29, Sample Test). Chrs makes annual deposts nto a bank account at the begnnng of each year for 20 years. Chrs ntal depost s equal to 100, wth each subsequent depost k% greater than the prevous year s depost. The bank credts nterest at an annual effectve rate of 5%. At the end of 20 years, the accumulated amount n Chrs account s equal to Gven k > 5, calculate k. A B C D E (# 5, November 2001). Mke buys a perpetuty mmedate wth varyng annual payments. Durng the frst 5 years, the payment s constant and equal to 10. Begnnng n year 6, the payments start to ncrease. For year 6 and all future years, the current year s payment s K% larger than the prevous year s payment. At an annual effectve nterest rate of 9.2%, the perpetuty has a present value of Calculate K, gven K < 9.2. (A) 4.0 (B) 4.2 (C) 4.4 (D) 4.6 (E) 4.8 7
8 38. (# 9, May 2000). A senor executve s offered a buyout package by hs company that wll pay hm a monthly beneft for the next 20 years. Monthly benefts wll reman constant wthn each of the 20 years. At the end of each 12month perod, the monthly benefts wll be adjusted upwards to reflect the percentage ncrease n the CPI. You are gven: () The frst monthly beneft s R and wll be pad one month from today. () The CPI ncreases 3.2% per year forever. At an annual effectve nterest rate of 6%, the buyout package has a value of 100, 000. Calculate R. (A) 517 (B) 538 (C) 540 (D) 548 (E) (# 45, May 2003). A perpetutymmedate pays 100 per year. Immedately after the ffth payment, the perpetuty s exchanged for a 25 year annuty mmedate that wll pay X at the end of the frst year. Each subsequent annual payment wll be 8% greater than the precedng payment. Immedately after the 10th payment of the 25 year annuty, the annuty wll be exchanged for a perpetutymmedate payng Y per year. The annual effectve rate of nterest s 8%. Calculate Y. (A) 110 (B) 120 (C) 130 (D) 140 (E) (# 51, May 2000). Seth deposts X n an account today n order to fund hs retrement. He would lke to receve payments of 50 per year, n real terms, at the end of each year for a total of 12 years, wth the frst payment occurrng seven years from now. The nflaton rate wll be 0.0% for the next sx years and 1.2% per annum thereafter. The annual effectve rate of return s 6.3%. Calculate X. (A) 303 (B) 306 (C) 316 (D) 327 (E) (# 22, May 2003). A perpetuty costs 77.1 and makes annual payments at the end of the year. The perpetuty pays 1 at the end of year 2, 2 at the end of year 3,... n at the end of year (n + 1). After year (n + 1), the payments reman constant at n. The annual effectve nterest rate s 10.5%. Calculate n. (A) 17 (B) 18 (C) 19 (D) 20 (E) (# 16, November 2001). Olga buys a 5 year ncreasng annuty for X. Olga wll receve 2 at the end of the frst month, 4 at the end of the second month, and for each month thereafter the payment ncreases by 2. The nomnal nterest rate s 9% convertble quarterly. Calculate X. (A) 2680 (B) 2730 (C) 2780 (D) 2830 (E) (# 26, May 2000). Betty borrows 19,800 from Bank X. Betty repays the loan by makng 36 equal payments of prncpal at the end of each month. She also pays nterest on the unpad 8
9 balance each month at a nomnal rate of 12%, compounded monthly. Immedately after the 16th payment s made, Bank X sells the rghts to future payments to Bank Y. Bank Y wshes to yeld a nomnal rate of 14%, compounded semannually, on ts nvestment. What prce does Bank X receve? (A) 9,792 (B) 10,823 (C) 10,857 (D) 11,671 (E) 11, (# 44, November 2000). Joe can purchase one of two annutes: Annuty 1: A 10 year decreasng annuty mmedate, wth annual payments of 10, 9, 8,..., 1. Annuty 2: A perpetuty mmedate wth annual payments. The perpetuty pays 1 n year 1, 2 n year 2, 3 n year 3,..., and 11 n year 11. After year 11, the payments reman constant at 11. At an annual effectve nterest rate of, the present value of Annuty 2 s twce the present value of Annuty 1. Calculate the value of Annuty 1. (A) 36.4 (B) 37.4 (C) 38.4 (D) 39.4 (E) (# 20, November 2000). Sandy purchases a perpetuty mmedate that makes annual payments. The frst payment s 100, and each payment thereafter ncreases by 10. Danny purchases a perpetuty due whch makes annual payments of 180. Usng the same annual effectve nterest rate, > 0, the present value of both perpetutes are equal. Calculate. (A) 9.2% (B) 9.7% (C) 10.2% (D) 10.7% (E) 11.2% 46. (# 30, Sample Test). Scott deposts: 1 at the begnnng of each quarter n year 1; 2 at the begnnng of each quarter n year 2; 8 at the begnnng of each quarter n year 8. One quarter after the last depost, Scott wthdraws the accumulated value of the fund and uses t to buy a perpetutymmedate wth level payments of X at the end of each year. All calculatons assume a nomnal nterest rate of 10% per annum compounded quarterly. Calculate X. A B C D E (# 7, May 2001). Seth, Jance, and Lor each borrow 5000 for fve years at a nomnal nterest rate of 12%, compounded sem annually. Seth has nterest accumulated over the fve years and pays all the nterest and prncpal n a lump sum at the end of fve years. 9
10 Jance pays nterest at the end of every sxmonth perod as t accrues and the prncpal at the end of fve years. Lor repays her loan wth 10 level payments at the end of every sxmonth perod. Calculate the total amount of nterest pad on all three loans. (A) 8718 (B) 8728 (C) 8738 (D) 8748 (E) (#28, Sample Test). A loan of 10, 000 s to be amortzed n 10 annual payments begnnng 6 months after the date of the loan. The frst payment, X, s half as large as the other payments. Interest s calculated at an annual effectve rate of 5% for the frst 4.5 years and 3% thereafter. Determne X. A. 640 B. 648 C. 656 D. 664 E (# 12, November 2002). Kevn takes out a 10 year loan of L, whch he repays by the amortzaton method at an annual effectve nterest rate of. Kevn makes payments of 1000 at the end of each year. The total amount of nterest repad durng the lfe of the loan s also equal to L. Calculate the amount of nterest repad durng the frst year of the loan. (A) 725 (B) 750 (C) 755 (D) 760 (E) (# 37, Sample Test). A loan s beng amortzed by means of level monthly payments at an annual effectve nterest rate of 8%. The amount of prncpal repad n the 12 th payment s 1000 and the amount of prncpal repad n the t th payment s Calculate t. A. 198 B. 204 C. 210 D. 216 E (# 10, May 2000). A bank customer borrows X at an annual effectve rate of 12.5% and makes level payments at the end of each year for n years. () The nterest porton of the fnal payment s () The total prncpal repad as of tme (n 1) s () The prncpal repad n the frst payment s Y. Calculate Y. (A) 470 (B) 480 (C) 490 (D) 500 (E) (# 24, May 2000). A small busness takes out a loan of 12, 000 at a nomnal rate of 12%, compounded quarterly, to help fnance ts startup costs. Payments of 750 are made at the end of every 6 months for as long as s necessary to pay back the loan. Three months before the 9th payment s due, the company refnances the loan at a nomnal rate of 9%, compounded monthly. Under the refnanced loan, payments of R are to be made monthly, wth the frst monthly payment to be made at the same tme that the 9th payment under the old loan was to be made. A total of 30 monthly payments wll completely pay off the loan. Determne R. (A) 448 (B) 452 (C) 456 (D) 461 (E)
11 53. (# 55, November 2000). Iggy borrows X for 10 years at an annual effectve rate of 6%. If he pays the prncpal and accumulated nterest n one lump sum at the end of 10 years, he would pay more n nterest than f he repad the loan wth 10 level payments at the end of each year. Calculate X. (A) 800 (B) 825 (C) 850 (D) 875 (E) (# 34, November 2000). An nvestor took out a loan of 150, 000 at 8% compounded quarterly, to be repad over 10 years wth quarterly payments of at the end of each quarter. After 12 payments, the nterest rate dropped to 6% compounded quarterly. The new quarterly payment dropped to After 20 payments n total, the nterest rate on the loan ncreased to 7% compounded quarterly. The nvestor decded to make an addtonal payment of X at the tme of hs 20th payment. After the addtonal payment was made, the new quarterly payment was calculated to be , payable for fve more years. Determne X. (A) 11, 047 (B) 13, 369 (C) 16, 691 (D) 20, 152 (E) 23, (# 37, May 2001). Seth borrows X for four years at an annual effectve nterest rate of 8%, to be repad wth equal payments at the end of each year. The outstandng loan balance at the end of the second year s and at the end of the thrd year s Calculate the prncpal repad n the frst payment. (A) 444 (B) 454 (C) 464 (D) 474 (E) (# 13, May 2001). Ron has a loan wth a present value of a n. The sum of the nterest pad n perod t plus the prncpal repad n perod t + 1 s X. Calculate X. (A) 1 + νn t (B) 1 + νn t d (C) 1 + ν n t (D) 1 + ν n t d (E) 1 + ν n t 57. (# 9, November 2001). A loan s amortzed over fve years wth monthly payments at a nomnal nterest rate of 9% compounded monthly. The frst payment s 1000 and s to be pad one month from the date of the loan. Each succeedng monthly payment wll be 2% lower than the pror payment. Calculate the outstandng loan balance mmedately after the 40th payment s made. (A) 6751 (B) 6889 (C) 6941 (D) 7030 (E) (# 36, Sample Test). Don takes out a 10year loan of L, whch he repays wth annual payments at the end of each year usng the amortzaton method. Interest on the loan s charged at an annual effectve rate of. Don repays the loan wth a decreasng seres of payments. He repays 1000 n year one, 900 n year two, 800 n year three,..., and 100 n year ten. The amount of prncpal repad n year three s equal to 600. Calculate L. A B C D E
12 59. (# 26, May 2001). Susan nvests Z at the end of each year for seven years at an annual effectve nterest rate of 5%. The nterest credted at the end of each year s renvested at an annual effectve rate of 6%. The accumulated value at the end of seven years s X. Lor nvests Z at the end of each year for 14 years at an annual effectve nterest rate of 2.5%. The nterest credted at the end of each year s renvested at an annual effectve rate of 3%. The accumulated value at the end of 14 years s Y. Calculate Y X. (A) 1.93 (B) 1.98 (C) 2.03 (D) 2.08 (E) (# 26, May 2003) s deposted nto Fund X, whch earns an annual effectve rate of 6%. At the end of each year, the nterest earned plus an addtonal 100 s wthdrawn from the fund. At the end of the tenth year, the fund s depleted. The annual wthdrawals of nterest and prncpal are deposted nto Fund Y, whch earns an annual effectve rate of 9%. Determne the accumulated value of Fund Y at the end of year 10. (A) 1519 (B) 1819 (C) 2085 (D) 2273 (E) (# 9, November 2000). Vctor nvests 300 nto a bank account at the begnnng of each year for 20 years. The account pays out nterest at the end of every year at an annual effectve nterest rate of %. The nterest s renvested at an annual effectve rate of ( 2) %. The yeld rate on the entre nvestment over the 20 year perod s 8% annual effectve. Determne. (A) 9% (B) 10% (C) 11% (D) 12% (E) 13% 62. (# 31, Sample Test). Jason deposts 3960 nto a bank account at t = 0. The bank credts nterest at the end of each year at a force of nterest δ t = 1. Interest can be renvested 8+t at an annual effectve rate of 7%. The total accumulated amount at tme t = 3 s equal to X. Calculate X. A B C D E (#33, Sample Test). Erc deposts 12 nto a fund at tme 0 and an addtonal 12 nto the same fund at tme 10. The fund credts nterest at an annual effectve rate of. Interest s payable annually and renvested at an annual effectve rate of At tme 20, the accumulated amount of the renvested nterest payments s equal to 64. Calculate, > 0. A. 8.8% B. 9.0% C. 9.2% D. 9.4% E. 9.6% 64. (# 39, May 2000). Sally lends 10, 000 to Tm. Tm agrees to pay back the loan over 5 years wth monthly payments payable at the end of each month. Sally can renvest the monthly payments from Tm n a savngs account payng nterest at 6%, compounded monthly. The yeld rate earned on Sally s nvestment over the fveyear perod turned out to be 7.45%, compounded semannually. What nomnal rate of nterest, compounded monthly, dd Sally 12
13 charge Tm on the loan? (A) 8.53% (B) 8.59% (C) 8.68% (D) 8.80% (E) 9.16% 65. (# 35, November 2001). At tme t = 0, Sebastan nvests 2000 n a fund earnng 8% convertble quarterly, but payable annually. He renvests each nterest payment n ndvdual separate funds each earnng 9% convertble quarterly, but payable annually. The nterest payments from the separate funds are accumulated n a sde fund that guarantees an annual effectve rate of 7%. Determne the total value of all funds at t = 10. (A) 3649 (B) 3964 (C) 4339 (D) 4395 (E) (# 4, May 2001). A 20 year loan of 20, 000 may be repad under the followng two methods: () amortzaton method wth equal annual payments at an annual effectve rate of 6.5% () snkng fund method n whch the lender receves an annual effectve rate of 8% and the snkng fund earns an annual effectve rate of j Both methods requre a payment of X to be made at the end of each year for 20 years. Calculate j. (A) j 6.5% (B) 6.5% < j 8.0% (C) 8.0% < j 10.0% (D) 10.0% < j 12.0% (E) j > 12.0% 67. (# 34, Sample Test). A 10 year loan of 10, 000 s to be repad wth payments at the end of each year consstng of nterest on the loan and a snkng fund depost. Interest on the loan s charged at a 12% annual effectve rate. The snkng fund s annual effectve nterest rate s 8%. However, begnnng n the sxth year, the annual effectve nterest rate on the snkng fund drops to 6%. As a result, the annual payment to the snkng fund s then ncreased by X. Calculate X. A. 122 B. 132 C. 142 D. 152 E (# 35, Sample Test). Jason and Margaret each take out a 17year loan of L. Jason repays hs loan usng the amortzaton method, at an annual effectve nterest rate of. He makes an annual payment of 500 at the end of each year. Margaret repays her loan usng the snkng fund method. She pays nterest annually, also at an annual effectve nterest rate of. In addton, Margaret makes level annual deposts at the end of each year for 17 years nto a snkng fund. The annual effectve rate on the snkng fund s 4.62%, and she pays off the loan after 17 years. Margaret s total payment each year s equal to 10% of the orgnal loan amount. Calculate L. A B C D E (# 48, November 2000). A 12 year loan of 8000 s to be repad wth payments to the lender of 800 at the end of each year and deposts of X at the end of each year nto a snkng fund. 13
14 Interest on the loan s charged at an 8% annual effectve rate. The snkng fund annual effectve nterest rate s 4%. Calculate X. (A) 298 (B) 330 (C) 361 (D) 385 (E) (# 6, November 2001). A 10 year loan of 2000 s to be repad wth payments at the end of each year. It can be repad under the followng two optons: () Equal annual payments at an annual effectve rate of 8.07%. () Installments of 200 each year plus nterest on the unpad balance at an annual effectve rate of. The sum of the payments under opton () equals the sum of the payments under opton (). Determne. (A) 8.75% (B) 9.00% (C) 9.25% (D) 9.50% (E) 9.75% 71. (# 15, May 2003). John borrows 1000 for 10 years at an annual effectve nterest rate of 10%. He can repay ths loan usng the amortzaton method wth payments of P at the end of each year. Instead, John repays the 1000 usng a snkng fund that pays an annual effectve rate of 14%. The deposts to the snkng fund are equal to P mnus the nterest on the loan and are made at the end of each year for 10 years. Determne the balance n the snkng fund mmedately after repayment of the loan. (A) 213 (B) 218 (C) 223 (D) 230 (E) (# 30, November, 2000). A 1000 par value 20 year bond wth annual coupons and redeemable at maturty at 1050 s purchased for P to yeld an annual effectve rate of 8.25%. The frst coupon s 75. Each subsequent coupon s 3% greater than the precedng coupon. Determne P. (A) 985 (B) 1000 (C) 1050 (D) 1075 (E) (# 41, May 2001). Bll buys a 10year 1000 par value 6% bond wth semannual coupons. The prce assumes a nomnal yeld of 6%, compounded semannually. As Bll receves each coupon payment, he mmedately puts the money nto an account earnng nterest at an annual effectve rate of. At the end of 10 years, mmedately after Bll receves the fnal coupon payment and the redempton value of the bond, Bll has earned an annual effectve yeld of 7% on hs nvestment n the bond. Calculate. (A) 9.50% (B) 9.75% (C) 10.00% (D) 10.25% (E) 10.50% 74. (# 31, November 2001). You have decded to nvest n two bonds. Bond X s an nyear bond wth semannual coupons, whle bond Y s an accumulaton bond redeemable n n 2 years. The desred yeld rate s the same for both bonds. You also have the followng nformaton: Bond X 14
15 Par value s r The rato of the semannual bond rate to the desred semannual yeld rate, s The present value of the redempton value s Bond Y Redempton value s the same as the redempton value of bond X. Prce to yeld s What s the prce of bond X? (A) 1019 (B) 1029 (C) 1050 (D) 1055 (E) (# 29, May 2000). A frm has proposed the followng restructurng for one of ts 1000 par value bonds. The bond presently has 10 years remanng untl maturty. The coupon rate on the exstng bond s 6.75% per annum pad semannually. The current nomnal semannual yeld on the bond s 7.40%. The company proposes suspendng coupon payments for four years wth the suspended coupon payments beng repad, wth accrued nterest, when the bond comes due. Accrued nterest s calculated usng a nomnal semannual rate of 7.40%. Calculate the market value of the restructured bond. (A) 755 (B) 805 (C) 855 (D) 905 (E) (#42, May 2003). A 10,000 par value 10year bond wth 8% annual coupons s bought at a premum to yeld an annual effectve rate of 6%. Calculate the nterest porton of the 7th coupon. (A) 632 (B) 642 (C) 651 (D) 660 (E) (#43, May 2000). A 1000 par value 5 year bond wth 8.0% semannual coupons was bought to yeld 7.5% convertble semannually. Determne the amount of premum amortzed n the 6th coupon payment. (A) 2.00 (B) 2.08 (C) 2.15 (D) 2.25 (E) (#38, Sample Test). Laura buys two bonds at tme 0. Bond X s a 1000 par value 14year bond wth 10% annual coupons. It s bought at a prce to yeld an annual effectve rate of 8%. Bond Y s a 14year par value bond wth 6.75% annual coupons and a face amount of F. Laura pays P for the bond to yeld an annual effectve rate of 8%. Durng year 6, the wrtedown n premum (prncpal adjustment) on bond X s equal to the wrteup n dscount (prncpal adjustment) on bond Y. Calculate P. A B C D E
16 79. (#39, Sample Test). A 1000 par value 18 year bond wth annual coupons s bought to yeld an annual effectve rate of 5%. The amount for amortzaton of premum n the 10th year s 20. The book value of the bond at the end of year 10 s X. Calculate X. A B C D E (# 40, November, 2000). Among a company s assets and accountng records, an actuary fnds a 15year bond that was purchased at a premum. From the records, the actuary has determned the followng: () The bond pays semannual nterest. () The amount for amortzaton of the premum n the 2nd coupon payment was () The amount for amortzaton of the premum n the 4th coupon payment was What s the value of the premum? (A) 17,365 (B) 24,784 (C) 26,549 (D) 48,739 (E) 50, (#48, May 2000). A corporaton buys a new machne for It has an expected useful lfe of 10 years, and a salvage value of 400. The machne s deprecated usng the snkng fund method and an annual effectve rate of. Deprecaton s taken at the end of each year for the 10 year perod. The present value of the deprecaton charges over the 10 year perod s 1000 at the annual effectve rate. Calculate. (A) 8.4% (B) 8.8% (C) 9.2% (D) 9.6% (E) 10.0% 82. (#42, November 2001). A coper costs X and wll have a salvage value of Y after n years. () Usng the straght lne method, the annual deprecaton expense s () Usng the sum of the years dgts method, the deprecaton expense n year 3 s 800. () Usng the declnng balance method, the deprecaton expense s % of the book value n the begnnng of the year. Calculate X. (A) 4250 (B) 4500 (C) 4750 (D) 5000 (E) (#45, November 2001). A manufacturer buys a machne for 20, 000. The manufacturer estmates that the machne wll last 15 years. It wll be deprecated usng the constant percentage method wth an annual deprecaton rate of 20%. At the end of each year, the manufacturer deposts an amount nto a fund that pays 6% annually. Each depost s equal to the deprecaton expense for that year. How much money wll the manufacturer have accumulated n the fund at the end of 15 years? (A) 29, 663 (B) 34, 273 (C) 36, 329 (D) 38, 509 (E) 46, (#5, May 2003). A machne s purchased for 5000 and has a salvage value of S at the end of 10 years. The machne s deprecated usng the sumoftheyearsdgts method. At 16
17 the end of year 4, the machne has a book value of At that tme, the deprecaton method s changed to the straghtlne method for the remanng years. Determne the new deprecaton charge for year 8. (A) 200 (B) 222 (C) 286 (D) 370 (E) (#11, May 2001). Machne I costs X, has a salvage value of X/8, and s to be deprecated over 10 years usng the declnng balance method. Machne II costs Y, has a salvage value of X/8, and s to be deprecated over 10 years usng the sum of the years dgts method. The total amount of deprecaton n the frst seven years for Machne I equals the total amount of deprecaton n the frst seven years for Machne II. Calculate Y. X (A) 0.94 (B) 0.99 (C) 1.04 (D) 1.09 (E) (# 8, November 2000) An actuary s tryng to determne the ntal purchase prce of a certan physcal asset. The actuary has been able to determne the followng: () Asset s 6 years old. () Asset s deprecated usng the snkng fund method, wth an annual effectve rate of 9%. () Book value of the asset after 6 years s 55, (v) The loss of nterest on the orgnal purchase prce s at an annual effectve rate of 9%. (v) Annual cost of the asset s 11, (v) Annual mantenance cost of the asset s What was the orgnal purchase prce of the asset? (A) 72,172 (B) 107,922 (C) 112,666 (D) 121,040 (E) 143, (# 36, May 2003) Erc and Jason each sell a dfferent stock short at the begnnng of the year for a prce of 800. The margn requrement for each nvestor s 50% and each wll earn an annual effectve nterest rate of 8% on hs margn account. Each stock pays a dvdend of 16 at the end of the year. Immedately thereafter, Erc buys back hs stock at a prce of (800 2X) and Jason buys back hs stock at a prce of (800 + X). Erc s annual effectve yeld,, on the short sale s twce Jason s annual effectve yeld. Calculate. (A) 4% (B) 6% (C) 8% (D) 10% (E) 12% 88. (# 27, May 2001) Jose and Chrs each sell a dfferent stock short for the same prce. For each nvestor, the margn requrement s 50% and nterest on the margn debt s pad at an annual effectve rate of 6%. Each nvestor buys back hs stock one year later at a prce of 760. Jose s stock pad a dvdend of 32 at the end of the year whle Chrs s stock pad no dvdends. Durng the 1year perod, Chrs s return on the short sale s, whch s twce 17
18 the return earned by Jose. Calculate. (A) 12% (B) 16% (C) 18% (D) 20% (E) 24% 2 Solutons 1. Snce each account earns an annual effectve dscount rate of d, each account earns the same annual effectve nterest rate. Bruce s nterest n the 11 th year s 100((1+) 11 (1+) 10 ) = 100(1 + ) 10. Robbe s nterest n the 17 th year s 50((1 + ) 17 (1 + ) 16 ) = 50(1 + ) 16. So, 100(1 + ) 10 = 50(1 + ) 16, (1 + ) 6 = 2, = 12.24% and x = 100(1 + ) 10 = 100(0.1224)( ) 10 = Erc s nterest s ( x 1 + 2) 16 ( x 1 + 2) 15 ( = x 1 + ) Mke s nterest s 2x 1 2 = x. So, (1 + 2 )15 = 2 and = %. 3. The followng seres of payments has present value zero: Contrbutons Tme Snce the rate changes at 10, we fnd the present value of the payments at ths tme. We have at tme 10, the followng seres of payments have the same value Contrbutons 10 Tme 0 Contrbutons Tme The present value at tme 10 of the payments at tme 15 and at tme 30 s 20(1.03) (1.03) 40 = = Ths equals the present value at tme 10 of the ntal depost,.e. 10 ( 1 d 4) 40 = So, d = %. 4. Let (2) be the nomnal semannual rate of Jennfer s loan. The future values of the loans are Dvdng these equatons ) 20 x (1 + (2) = 800 and x ( 1 + (2)) 20 = ( 1 + (2) 1 + (2) 2 ) 20 = = 1.4. So, (2) = (1.4)1/ (1.4)1/20 2 = and x = 1120 ( ) 20 =
19 5. Snce s a nomnal rate of nterest convertble semannually, 100(1 + 2 )(2)(7.25) = 200 and = %. To fnd the force of nterest, we solve for δ, 100e δ(7.25) = 200, and get δ = We have that δ = = = 0.23%. 6. For Fund X, A(t) = 10000( ) t and δ t = d ln A(t) = ln(1.05). For Fund Y, A(t) = dt 10000(1 + (0.08)t) and δ t = d 0.08 ln A(t) =. The two forces of nterest are equal, when, dt t ln(1.05) = The soluton of ths equaton s t = 1 1 = 8. For Fund X, t ln(1.05) 0.08 A(8) = 10000( ) 8 = For Fund Y, A(8) = 10000(1 + (0.08)8) = So, Z = = We have that ( a(t) = e R t ) ( ) t t 0 δs ds 2 = exp 0 k + 2s ds = exp ln(k + 2s) The nformaton says that 0 = e ln(k+2t) ln k = k + 2t. k x = 75a(3) = 75(k + 6), x = 150 a(3) k a(5) = 150(k + 6) k Dvdng these two equatons, 1 = k+10 2k and k = 10. So, x = 75(k+6) k = = Frst, we fnd a(4) = e R 4 0 δs ds : 4 0 δ s ds = 3 0 (0.02)s ds (0.045) ds = (0.02)s (0.045)s = and a(4) = e Let (4) be the nomnal rate of nterest compounded quarterly. Then, ( ) 4 4 ( ) 16. a(4) = 1 + (4) 4 = 1 + (4) 4 So, (4) = 4(e 0.135/16 1) = = %. 9. We have that for Fund X, ( ) a(t) = e R t 0 δs ds = e R t t 0 (0.006)s2 ds = exp (0.002)s 3 = e (0.002)t3 = e t3 /500. For Fund X, 4K = A(n) = A(0)a(n) = Ke n3 /500. So, n = (500 ln 4) 1/3 = For Fund Y, a(t) = ( ) t. So, 4K = A(n) = a(n) A(m) = (1 + a(m) 0.10)n m 2K. So, n m = ln 2 = Hence, m = = ln For the Fund X, a(5) = e R 5 0 δs ds = e R 5 s 2 0 k ds = e 125/(3k). For the Fund Y, a(5) = ( ) (2) 5 = (0.96) 10. From the equaton, e 125/(3k) = (0.96) 10, we get that k = 125 (3)(10)(ln 0.96) =
20 11. For Tawny s bank account, a(t) = ( ) t = (1.05) 2t and the force of nterest s δ t = d ln a(t) = 2 ln(1.05). For Fabo s account, a(t) = 1 + t and δ dt t = 2 ln(1.05) = 2 ln(1.05). So, = = So, ln(1.05) 2 Z = A(5) = A(0)(1 + t) = 1000 (1 + 5 (0.1905)) = At tme t = 5, 1+t 12. The value of Joe s deposts at tme 10 s 10 (1 + (0.11)(10 0)) + 30 (1 + (0.11)(10 5)) = = The value of Tna s deposts at tme 10 s 10( ) 10 n + 30( ) 10 2n. Call x = (1.0915) n. Then, 10( ) 10 x + 30( ) 10 x 2 = So, 3x 2 + x = (67.5) 10 1 (1.0915) 10 = So, (1.0915) n = x = 1± 1 2 +(4)(3)(2.8123) = (2)(3) and n = We have that a(t) = e R t 0 δs ds = e R t s ds = e t The accumulaton of the nvestments at tme t = 3 s 100a(3) + x. The accumulaton of the nvestments at tme t = 6 s a(6) (100a(3) + x). The amount of nterest earned from a(3) tme 3 to tme 6 s x = a(6) a(6) a(3) (100a(3) + x) (100a(3) + x) = (100a(3) + x). a(3) a(3) Solvng for x, we get that = 100 e 3 3 2a(3) a(6) x = 100 a(3)(a(6) a(3)) 2e e = (100)( )( ) = (2)( ) (e e ) 14. Snce the equatons of value of the two streams of payments at tme zero are equal, Usng that ν n = , we have that So, = 3.51% ν n + 300ν 2n = 600ν (1 + ) 10 = 600ν 10 = ( ) + 300( ) 2 =
10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose
More informationSection 2.3 Present Value of an Annuity; Amortization
Secton 2.3 Present Value of an Annuty; Amortzaton Prncpal Intal Value PV s the present value or present sum of the payments. PMT s the perodc payments. Gven r = 6% semannually, n order to wthdraw $1,000.00
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More informationSection 2.2 Future Value of an Annuity
Secton 2.2 Future Value of an Annuty Annuty s any sequence of equal perodc payments. Depost s equal payment each nterval There are two basc types of annutes. An annuty due requres that the frst payment
More information3. Present value of Annuity Problems
Mathematcs of Fnance The formulae 1. A = P(1 +.n) smple nterest 2. A = P(1 + ) n compound nterest formula 3. A = P(1.n) deprecaton straght lne 4. A = P(1 ) n compound decrease dmshng balance 5. P = 
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More information8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value
8. Annutes: Future Value YOU WILL NEED graphng calculator spreadsheet software GOAL Determne the future value of an annuty earnng compound nterest. INVESTIGATE the Math Chrstne decdes to nvest $000 at
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationMathematics of Finance
Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY
More informationMathematics of Finance
5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty;Amortzaton Chapter 5 Revew Extended Applcaton:Tme, Money, and Polynomals Buyng a car
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount in the account, the balance, is
Payout annutes: Start wth P dollars, e.g., P = 100, 000. Over a 30 year perod you receve equal payments of A dollars at the end of each month. The amount of money left n the account, the balance, earns
More informationAS 2553a Mathematics of finance
AS 2553a Mathematcs of fnance Formula sheet November 29, 2010 Ths ocument contans some of the most frequently use formulae that are scusse n the course As a general rule, stuents are responsble for all
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 151. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationCompound Interest: Further Topics and Applications. Chapter 9
92 Compound Interest: Further Topcs and Applcatons Chapter 9 93 Learnng Objectves After letng ths chapter, you wll be able to:? Calculate the nterest rate and term n ound nterest applcatons? Gven a nomnal
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationInterest Rate Futures
Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationChapter 15: Debt and Taxes
Chapter 15: Debt and Taxes1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationChapter 4 Financial Markets
Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (nm) months, startng n m months: Example: Depostor wants to fx rate
More informationUncrystallised funds pension lump sum payment instruction
For customers Uncrystallsed funds penson lump sum payment nstructon Don t complete ths form f your wrapper s derved from a penson credt receved followng a dvorce where your ex spouse or cvl partner had
More informationDISCLOSURES I. ELECTRONIC FUND TRANSFER DISCLOSURE (REGULATION E)... 2 ELECTRONIC DISCLOSURE AND ELECTRONIC SIGNATURE CONSENT... 7
DISCLOSURES The Dsclosures set forth below may affect the accounts you have selected wth Bank Leum USA. Read these dsclosures carefully as they descrbe your rghts and oblgatons for the accounts and/or
More informationAmeriprise Financial Services, Inc. or RiverSource Life Insurance Company Account Registration
CED0105200808 Amerprse Fnancal Servces, Inc. 70400 Amerprse Fnancal Center Mnneapols, MN 55474 Incomng Account Transfer/Exchange/ Drect Rollover (Qualfed Plans Only) for Amerprse certfcates, Columba mutual
More informationThe CoxRossRubinstein Option Pricing Model
Fnance 400 A. Penat  G. Pennacc Te CoxRossRubnsten Opton Prcng Model Te prevous notes sowed tat te absence o arbtrage restrcts te prce o an opton n terms o ts underlyng asset. However, te noarbtrage
More informationBond futures. Bond futures contracts are futures contracts that allow investor to buy in the
Bond futures INRODUCION Bond futures contracts are futures contracts that allow nvestor to buy n the future a theoretcal government notonal bond at a gven prce at a specfc date n a gven quantty. Compared
More informationTrivial lump sum R5.0
Optons form Once you have flled n ths form, please return t wth your orgnal brth certfcate to: Premer PO Box 2067 Croydon CR90 9ND. Fll n ths form usng BLOCK CAPITALS and black nk. Mark all answers wth
More informationConstruction Rules for Morningstar Canada Target Dividend Index SM
Constructon Rules for Mornngstar Canada Target Dvdend Index SM Mornngstar Methodology Paper October 2014 Verson 1.2 2014 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM0905. January 14, 2014: Questions and solutions 58 60 were
More informationEffective December 2015
Annuty rates for all states EXCEPT: NY Prevous Index Annuty s effectve Wednesday, December 7 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt Spread MLSB 2Yr Pt to Pt Spread 3 (Annualzed)
More informationADVA FINAN QUAN ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS VAULT GUIDE TO. Customized for: Jason (jason.barquero@cgu.edu) 2002 Vault Inc.
ADVA FINAN QUAN 00 Vault Inc. VAULT GUIDE TO ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS Copyrght 00 by Vault Inc. All rghts reserved. All nformaton n ths book s subject to change wthout notce. Vault
More information= i δ δ s n and PV = a n = 1 v n = 1 e nδ
Exam 2 s Th March 19 You are allowe 7 sheets of notes an a calculator 41) An mportant fact about smple nterest s that for smple nterest A(t) = K[1+t], the amount of nterest earne each year s constant =
More informationEffective September 2015
Annuty rates for all states EXCEPT: NY Lock Polces Prevous Prevous Sheet Feld Bulletns Index Annuty s effectve Monday, September 28 Global Multple Index Cap S&P Annual Pt to Pt Cap MLSB Annual Pt to Pt
More informationUncrystallised funds pension lump sum
For customers Uncrystallsed funds penson lump sum Payment nstructon What does ths form do? Ths form nstructs us to pay the full penson fund, under your nonoccupatonal penson scheme plan wth us, to you
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationProperties of American Derivative Securities
Capter 6 Propertes of Amercan Dervatve Securtes 6.1 Te propertes Defnton 6.1 An Amercan dervatve securty s a sequence of nonnegatve random varables fg k g n k= suc tat eac G k s F k measurable. Te owner
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationAccount Transfer and Direct Rollover
CED0105 Amerprse Fnancal Servces, Inc. 70100 Amerprse Fnancal Center Mnneapols, MN 55474 Account Transfer and Drect Rollover Important: Before fnal submsson to the Home Offce you wll need a Reference Number.
More informationREQUIRED FOR YEAR END 31 MARCH 2015. Your business information
REQUIRED FOR YEAR END 31 MARCH 2015 Your busness nformaton Your detals Busness detals Busness name Balance date IRD number Contact detals  to ensure our records are up to date, please complete the followng
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationReporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide
Reportng Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (ncludng SME Corporate), Soveregn and Bank Instructon Gude Ths nstructon gude s desgned to assst n the completon of the FIRB
More informationReporting Instructions for Schedules A through S
FFIEC 0 Reportng Instructons for Schedules A through S FFIEC 0 FFIEC 0 CONTENTS INSTRUCTIONS FOR PREPARATION OF FFIEC 0 RskBased Captal Reportng for Insttutons Subject to the Advanced Captal Adequacy
More informationA Critical Note on MCEV Calculations Used in the Life Insurance Industry
A Crtcal Note on MCEV Calculatons Used n the Lfe Insurance Industry Faban Suarez 1 and Steven Vanduffel 2 Abstract. Snce the begnnng of the development of the socalled embedded value methodology, actuares
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationCapital asset pricing model, arbitrage pricing theory and portfolio management
Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securtyspecfc rsk
More informationVariable Payout Annuities with Downside Protection: How to Replace the Lost Longevity Insurance in DC Plans
Varable Payout Annutes wth Downsde Protecton: How to Replace the Lost Longevty Insurance n DC Plans By: Moshe A. Mlevsky 1 and Anna Abamova 2 Summary Abstract Date: 12 October 2005 Motvated by the rapd
More informationTrust Deed UNISAVER NEW ZEALAND
Trust Deed UNISAVER NEW ZEALAND Table of contents Partes...1 Background...1 Operatve Part...1 Covenants...2 1 Establshment of Scheme...2 2 Defntons and Interpretaton...2 3 Membershp...10 4 Contrbutons...10
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationAnnuity is defined as a sequence of n periodical payments, where n can be either finite or infinite.
1 Annuity Annuity is defined as a sequence of n periodical payments, where n can be either finite or infinite. In order to evaluate an annuity or compare annuities, we need to calculate their present value
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationCHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY. Themes of the chapter. Nominal rigidities, expectational errors and employment fluctuations
CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY Themes of the chapter Nomnal rgdtes, expectatonal errors and employment fluctuatons The shortrun tradeoff between nflaton and unemployment The
More informationMorningstar AfterTax Return Methodology
Mornngstar AfterTax Return Methodology Mornngstar Research Report March 1, 2013 2013 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property of Mornngstar, Inc. Reproducton or
More informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets holdtomaturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationNordea G10 Alpha Carry Index
Nordea G10 Alpha Carry Index Index Rules v1.1 Verson as of 10/10/2013 1 (6) Page 1 Index Descrpton The G10 Alpha Carry Index, the Index, follows the development of a rule based strategy whch nvests and
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationPerformance attribution for multilayered investment decisions
Performance attrbuton for multlayered nvestment decsons 880 Thrd Avenue 7th Floor Ne Yor, NY 10022 212.866.9200 t 212.866.9201 f qsnvestors.com Inna Oounova Head of Strategc Asset Allocaton Portfolo Management
More information