# 10.2 Future Value and Present Value of an Ordinary Simple Annuity

Save this PDF as:

Size: px
Start display at page:

Download "10.2 Future Value and Present Value of an Ordinary Simple Annuity"

## Transcription

1 348 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 made at the end of each payment perod and the compoundng perod s equal to the payment perod. In ths secton, you wll learn how to calculate the future value and present value of an ordnary smple annuty. Future Value of an Ordnary Smple Annuty Consder an example where Abrella decdes to nvest \$1000 at the end of every year for fve years n a savngs account that earns an nterest rate of 10% compounded annually. She wants to fnd out how much she would have at the end of the fve-year perod. In other words, she wants to fnd out the future value of her nvestments at the end of fve years. To calculate the future value of her nvestments at the end of fve years, we could calculate the future value of each of her nvestments usng the compound nterest formula and then add all the future values. From the compound nterest Formula 9.1(a), we know that the future value of each payment s FV = PV(1 + ) n where, FV = future value, PV = present value, = nterest rate for the compoundng perod (perodc nterest rate), and n = total number of compoundng perods for each payment. In ths example: 'PV' for each payment s \$1000 j 010. '' for each payment s = = = 0.10 per annum m 1 'n' for each payment s not the same. 'n' for each payment startng from the 1 st payment s 4, 3, 2, 1, and 0. The future value of an annuty s the sum of the accumulated value of each perodc payment. Indvdual future values calculated are n geometrc seres wth 'n' terms, where the 1 st term s PMT and the common rato s (1+). By applyng the formula for the sum of a geometrc seres you wll get the smplfed 'FV' Formula 10.2 (a). Exhbt 10.2(a): Future Value of Ordnary Smple Annuty Payments Sum of the future values of her nvestment = = \$ Therefore, f she nvests \$1000 every year for fve years at 10% compounded annually n a savngs account, she would have a total of \$ at the end of fve years.

2 Chapter 10 Annutes 349 Now, f there were many payments for an annuty (e.g., she nvested the same amount for 15 years, compounded annually), the above method would become too tme-consumng. A smplfed formula to calculate the future value of an ordnary smple annuty s gven by: Formula 10.2(a) Future Value of an Ordnary Smple Annuty FV = PMT In an annuty, 'n' s the number of payments durng the term. Example 10.2(a) where 'n' s the number of payments durng the term, 'PMT' s the amount of the perodc payment, and '' s the perodc nterest rate. Calculatng the future value of her nvestment at the end of fve years usng ths smplfed formula, n = 1 payment/year # 5 years = 5 annual payments j 010. = = = 0.10 m 1 PMT = \$1000 n ^1+ h - 1 FV = PMT ; E 5 ^ h - 1 = 1000; E 010. = 1000 [6.1051] = \$ Therefore, the future value of the nvestment s \$ In the calculaton of the future value of annutes, the amount of nterest s calculated as follows: Amount of Interest Earned = Future Value of the Investments - Amount Invested Over the Term I = FV - n(pmt) In ths example, I = ( ) = = \$ Therefore, she would earn \$ from ths nvestment. Calculatng the Future Value, Total Investment, and Interest Earned n an Ordnary Smple Annuty Rta nvested \$200 at the end of every month for 20 years nto an RRSP. Assume that the nterest rate was constant at 6% compounded monthly over the entre term. () What was the accumulated value of the nvestment at the end of the term? () What was the total nvestment over the term? () What was the amount of nterest earned? Ths s an ordnary smple annuty as: Payments are made at the end of each payment perod (monthly) Compoundng perod (monthly) = payment perod (monthly)

3 350 Chapter 10 Annutes contnued () Usng Formula 10.2(a), ^1+ h n - 1 FV = PMT ; E 240 ^ h - 1 = 200 ; E = 200 [ ] = \$92, Therefore, the accumulated value of the nvestment at the end of the term was \$92, () Total Investment = \$200 per month # 240 payments = \$48, Therefore, the total nvestment over the term was \$48, () Interest Earned = \$92, \$48, = \$44, Therefore, the amount of nterest earned was \$44, Usng the Fnancal Calculator to Solve Problems Before you start solvng problems, check and set the followng n the Texas Instruments BA II Plus fnancal calculator: 1. Set the number of decmals to 9. (Set ths only when you start usng the calculator.) Press 2ND then press FORMAT (ths s the secondary functon of the decmal key). Enter 9 then press ENTER to set the number of decmals to 9. Press 2ND then QUIT (ths s the secondary key above CPT). 2. Check the settngs for end-of-perod (ordnary annuty) or begnnng-of-perod (annuty due) calculatons. (You need to check ths before you work out problems.) Pressng 2ND then BGN (secondary functon above PMT) wll dsplay the current settng - ether END or BGN. (Select END for ordnary annuty problems and BGN for annuty due problems.) END would mean end-of-perod settng (for an ordnary annuty). To change ths settng to begnnng-of-perod settng (for annuty due), press 2ND then SET (secondary functon above ENTER). You can swtch between END and BGN by pressng 2ND then SET agan. If BGN settng s selected, a small BGN appears at the top-rght corner of your screen and wll reman there throughout your calculatons. However, f END s selected, nothng wll appear. Once you select your settng, press 2ND then QUIT (secondary functon above CPT) and return to your calculaton.

4 Chapter 10 Annutes 351 Solvng Example 10.2(a)() usng the Texas Instruments BA II Plus calculator, to fnd 'FV' Where, P/Y = 12, C/Y = 12, N = 240, I/Y = 6, PMT = \$200 Cash-Flow Sgn Conventon Transacton PV FV Investment Outflow (-) Inflow (+) Clear past values n the memory of the functon keys. Ths opens the P/Y, C/Y worksheet to set values. Set payments per year (P/Y) equal to compoundng perods per year (C/Y) as 12. You can scroll down usng the down arrow key to vew C/Y, whch wll be automatcally set to 12. Ths closes the P/Y, C/Y worksheet. Number of payments (n). Nomnal nterest rate per year (j). In annuty problems, we wll usually fnd ether FV or PV. To avod errors when you are fndng FV set PV to 0 and vce versa. Perodc payments can be cash nflows or outflows, so set the sgn accordngly. In ths problem, t s a cash outflow (money pad out for the nvestment), therefore, the perodc payment s negatve. Loan Inflow (+) Outflow (-) Example 10.2(b) When the payment date of the nvestment s not stated, t s assumed to be at the end of the payment perod. Calculatng the Future Value, Total Investment, and Interest Earned n an Ordnary Smple Annuty Combned wth a Compound Interest Perod Jack deposted \$1500 nto an account every three months for a perod of four years. He then let the money grow for another sx years wthout nvestng any more money nto the account. The nterest rate on the account was 6% compounded quarterly for the frst four years and 9% compounded quarterly for the next sx years. Calculate () the accumulated amount of money n the account at the end of the 10-year perod and () the total nterest earned. Ths s an ordnary smple annuty as: Payments are assumed to be at the end of each payment perod (quarterly) Compoundng perod (quarterly) = payment perod (quarterly)

5 352 Chapter 10 Annutes contnued () Usng Formula 10.2(a), n ^1+ h - 1 FV = PMT ; E FV 1 = 1500 = ^ h G = 1500[ ] = \$26, Ths 'FV 1 ' amount now becomes the present value for the compoundng perod. We now need to fnd the future value of ths amount usng the compound nterest formula. FV 2 = PV 2 (1 + ) n Here, 'n', the number of compoundng perods = m # t = 24 FV 2 = 26, ( ) 24 = \$45, Therefore, the accumulated amount of money n the account at the end of the 10-year perod was \$45, () Total Invested = n(pmt) = 16 # = \$24, Interest Earned = FV - n(pmt) = 45, , = \$21, Therefore, the total nterest earned over the perod was \$21, Example 10.2(c) Calculatng the Future Value when Payment Changes Grace saved \$500 at the end of every month n an RRSP for fve years and thereafter \$600 at the end of every month for the next three years. If the nvestment was growng at 3% compounded monthly, calculate the maturty value of her RRSP at the end of eght years. Ths s an ordnary smple annuty as: Payments are made at the end of each payment perod (monthly) Compoundng perod (monthly) = payment perod (monthly)

6 Chapter 10 Annutes 353 contnued Calculatng the future value of PMT () at the end of the fve years Usng Formula 10.2(a), n ^1+ h - 1 FV = PMT ; E FV 1 = ^ h -1 ; E = 500[ ] = \$32, FV 1 becomes the present value for the compoundng perod. We now need to fnd the future value of ths amount usng the compound nterest formula. FV 2 = PV 2 (1 + ) n Here 'n', the number of compoundng perods = m # t = 36 FV 2 = 32, ( ) 36 = \$35, Calculatng the future value of PMT () at the end of the term: Usng Formula 10.2(a), n ^1+ h - 1 FV = PMT ; E ^ h -1 FV 3 = 600 ; E = 600[ ] = \$22, Maturty value of nvestment at the end of the term: = FV 2 + FV 3 = 35, , =\$57, Therefore, the maturty value of her nvestment at the end of eght years s \$57, Present Value of an Ordnary Smple Annuty Consder an example where Margaret wshes to wthdraw \$1000 at the end of every year for the next fve years from an account that pays nterest at 10% compounded annually. How much money should she depost nto ths account now? To calculate the present value of all the payments at the begnnng of the fve-year perod, we can calculate the present value of each payment and then add all the present values usng the compound nterest formula as shown below: As payments that she would be recevng n the future have to be dscounted, the present value of FV each payment s gven by the compound nterest formula: PV = n = FV(1 + ) -n ^1 + h where 'n' s the number of compoundng perods for each payment. 'n' for each payment startng from the 1 st payment s 1,2,3,4, and 5.

7 354 Chapter 10 Annutes Indvdual present values calculated are n geometrc seres wth 'n' terms, where the 1 st term s 'PMT' and the common rato s (1+ ) -1. By applyng the formula for the sum of a geometrc seres you wll get the smplfed 'PV' Formula 10.2 (b). The present value of an annuty s the sum of the dscounted values of each perodc payment. Formula 10.2(b) Exhbt 10.2(b): Present Value of Ordnary Smple Annuty Payments Sum of Present Values of her Investment = = \$ Now, smlar to the smplfed formula used n FV calculatons, the smplfed PV formula s gven by: Present Value of an Ordnary Smple Annuty PV = PMT where 'n' s the number of payments durng the term and 'PMT' s the perodc payment. Calculatng the present value of her payments usng ths smplfed formula: 1- ^ h 5 PV = 1000 ; E = 1000[ ] 0.10 = \$ Therefore, she would have to depost \$ at the begnnng of the fve-year perod to be able to wthdraw \$1000 at the end of each year for fve years. In calculatng the present value of an annuty, the amount of nterest s calculated as follows: Amount of Interest Earned = Amount Receved over the Term - Present Value I = n(pmt) - PV In ths example, I = 5( ) - \$ = \$ = \$ Therefore, she would earn nterest of \$ Example 10.2(d) Calculatng the Present Value and Interest Earned n an Ordnary Smple Annuty Zack purchased an annuty that provded hm wth payments of \$1000 every month for 25 years at 5.4% compounded monthly. () How much dd he pay for the annuty? () What was the total amount receved from the annuty and how much of ths amount was the nterest earned? Ths s an ordnary smple annuty as: Payments are assumed to be made at the end of each payment perod (monthly) Compoundng perod (monthly) = payment perod (monthly)

8 Chapter 10 Annutes 355 contnued () Usng Formula 10.2(b), 1- ^1+ h - n PV = PMT ; E 1- ^ h 300 = 1000 ; E = 1000 [ ] = \$164, Therefore, he pad \$164, for the annuty. () Amount Receved = n(pmt) = 300 # \$ = \$300, Interest Earned = n(pmt) - PV = 300, , = \$135, Example 10.2(e) Calculatng the Present Value, Amount Invested, and Total Interest Charged n an Ordnary Smple Annuty Andrew pad \$20,000 as a down payment towards the purchase of a machne and receved a loan for the balance amount at an nterest rate of 3% compounded monthly. He settled the loan n ten years by payng \$1500 at the end of every month. () What was the purchase prce of the machne? () What was the total amount pad to settle the loan and what was the amount of nterest charged? Ths s an ordnary smple annuty as: Payments are made at the end of each payment perod (monthly) Compoundng perod (monthly) = payment perod (monthly)

9 356 Chapter 10 Annutes contnued () Usng Formula 10.2(b), - n 1- ^1+ h PV = PMT ; E 1. = ^ h ; 120 E = 1500[ ] = 155, = \$155, As he pad \$20, as down payment for the machne: Purchase Prce = Down Payment + PV of All Payments = 20, , = \$175, Therefore, the purchase prce of the machne was \$175, () Calculatng the total amount pad and the nterest amount Amount Pad = n(pmt) = 120 # = \$180, Interest Charged = n(pmt) - PV = 180, , = \$24, Therefore, the total amount pad to settle the loan was \$180, and the amount of nterest charged was \$24, Example 10.2(f) Calculatng the Present Value when the Interest Rate Changes How much should Halfax Steel Inc. nvest today n a fund to be able to wthdraw \$15,000 at the end of every three months for a perod of sx years? The money n the fund s expected to grow at 4.8% compounded quarterly for the frst two years and 5.6% compounded quarterly for the next four years. Ths s an ordnary smple annuty as: Wthdrawals are made at the end of each payment perod (quarterly) Compoundng perod (quarterly) = payment perod (quarterly)

10 Chapter 10 Annutes 357 contnued Calculatng PV when nterest rate s 4.8% compounded quarterly Usng Formula 10.2(b), - n 1- ^1+ h PV = PMT ; E PV 1 = 15,000 ; 1 - ( ) E = 15,000[ ] = \$113, Calculatng PV when nterest rate s 5.6% compounded quarterly Usng Formula 10.2(b), - n 1- ^1+ h PV = PMT ; E PV 2 = 15,000 ; 1 - ( ) E = 15,000[ ] = \$213, PV 2 becomes the future value for the compounded perod. We now need to fnd the present value of that amount usng the compound nterest formula. PV 3 = FV 3 (1 + ) -n Intal value of the nvestment = 213, ( ) -8 = \$194, = PV 1 + PV 3 = 113, , = 308, Therefore, n order to be able to wthdraw \$15,000 at the end of every three months for sx years, Halfax Steel Inc. should nvest \$308, today Exercses Answers to the odd-numbered problems are avalable at the end of the textbook 1. Calculate the future value of each of the followng ordnary smple annutes: Perodc Payment Payment Perod Term of Annuty Interest Rate Compoundng Frequency a. \$2500 Every year 10 years 4.50% Annually b. \$1750 Every 6 months 7.5 years 5.10% Sem-annually c. \$900 Every 3 months 5 years 4.60% Quarterly d. \$475 Every month 4.5 years 6.00% Monthly

11 358 Chapter 10 Annutes 2. Calculate the future value of each of the followng ordnary smple annutes: Perodc Payment Payment Perod Term of Annuty Interest Rate Compoundng Frequency a. \$4500 Every year 12 years 4.75% Annually b. \$2250 Every 6 months 6 years 5.00% Sem-annually c. \$800 Every 3 months 8.5 years 4.80% Quarterly d. \$350 Every month 10 years 3 months 5.76% Monthly 3. Calculate the present value of each of the ordnary smple annutes n Problem Calculate the present value of each of the ordnary smple annutes n Problem Alana saved \$50 at the end of every month n her savngs account at 6% compounded monthly for fve years. a. What s the accumulated value of the money at the end of fve years? b. What s the nterest earned? 6. Sharleen contrbuted \$400 towards an RRSP at the end of every month for four years at 2.5% compounded monthly. a. What s the accumulated value of the money at the end of four years? b. What s the nterest amount earned? 7. Shanelle saves \$600 at the end of every month n an RESP at 4.5% compounded monthly for 15 years for her chld's educaton. a. How much wll she have at the end of 15 years? b. If she leaves the accumulated money n the savngs account for another two years, earnng the same nterest rate, how much wll she have at the end of the perod? 8. Lue makes deposts of \$250 at the end of every month for ten years n a savngs account at 3.5% compounded monthly. a. How much wll he have at the end of ten years? b. If he plans to leave the accumulated amount n the account for another fve years at the same nterest rate, how much wll he have at the end of the perod? 9. Carre saved \$750 of her salary at the end of every month n an RRSP earnng 4% compounded monthly for 20 years. How much more would she have earned f she had saved ths amount n an RRSP that was earnng an nterest rate of 4.25% compounded monthly? 10. Adran nvests \$500 at the end of every three months n a savngs account at 6% compounded quarterly for 7 years and 9 months. How much more would he have earned f he had saved t n a fund that was provdng an nterest rate of 6.5% compounded quarterly? 11. What s the dscounted value of the followng stream of payments: \$3000 receved at the end of every 3 months for 10 years and 6 months at 3% compounded quarterly? 12. What s the dscounted value of the followng stream of payments: \$1250 receved at the end of every month for 3 years and 2 months? Assume that money s worth 2.75% compounded monthly. 13. How much should Cortland have n a savngs account that s earnng 4% compounded monthly f he plans to wthdraw \$1500 from the account at the end of every month for ten years? 14. Calculate the amount of money that Chn Ho should depost n an nvestment account that s growng at 6% compounded monthly to be able to wthdraw \$700 at the end of every month for four years.

12 Chapter 10 Annutes Adler took a loan from a bank at 7% compounded monthly to purchase a car. He was requred to pay the bank \$300 at the end of every month for the next three years. What was the cash prce of the car? 16. What would be the purchase prce of an annuty that provdes \$500 at the end of every month for fve years and earns an nterest rate of 4% compounded monthly? 17. Calculate the accumulated value of annuty contrbutons of \$500 at the end of every month for fve years followed by contrbutons of \$750 at the end of every month for the next four years f money s worth 4.2% compounded monthly. 18. Kumar nvested \$1000 at the end of every sx months for sx years followed by \$1250 at the end of every sx months for the next three years nto a fund that earns 3.25% compounded sem-annually. Calculate the accumulated amount at the end of nne years. 19. Donovan contrbuted \$900 at the end of every three months for seven years nto an RRSP fund that earned nterest at 3.9% compounded quarterly for the frst four years and 3.8% compounded quarterly for the next three years. Calculate the accumulated value of the contrbuton at the end of seven years and the amount of nterest earned. 20. Calculate the accumulated value and the amount of nterest earned on deposts of \$125 made at the end of every month nto an RESP fund for 12 years f the fund earned nterest at 3.75% compounded monthly for 7 years and 4.35% compounded monthly for the next 5 years. 21. Jordan nvested \$1500 at the end of every sx months for four years and then \$750 at the end of every three months for the next two years. The nvestment earned nterest at 5% compounded sem-annually the frst four years and 4.8% compounded quarterly for the next two years. Calculate the accumulated value at the end of sx years and the amount of nterest earned. 22. Calculate the accumulated value of an annuty wth payments of \$1500 at the end of every three months for three years at 4.1% compounded quarterly and \$1750 at the end of every three months for the next two years at 4.25% compounded quarterly. 23. Falco Inc. pad \$25,000 as a down payment for a machne. The balance amount was fnanced wth a loan at 3.25% compounded sem-annually, whch requred a payment of \$9000 at the end of every sx months for fve years to settle the loan. a. What was the purchase prce of the machne? b. What was the total amount of nterest charged? 24. Brandon purchased a computer-controlled machne for hs machne shop by payng a down payment of \$17,500. He fnanced the balance amount wth a loan at 4.75% compounded sem-annually, whch requred a payment of \$10,000 at the end of every sx months for three years. a. What was the purchase prce of the machne? b. What was the total amount of nterest charged? 25. How much would you have to pay now for a retrement annuty that would provde \$3000 at the end of every three months at 5% compounded quarterly for the frst ten years and \$2500 at the end of each month at 6% compounded monthly for the followng fve years? 26. How much should Drake pay today for a retrement annuty that would provde hm wth \$4000 at the end of every month for fve years at 3.5% compounded monthly and \$20,000 every sx months for the next ten years at 4% compounded sem-annually? 27. Kayla wanted to purchase a storage locker for \$5000 at her apartment buldng. She could ether pay the entre amount or take a loan from the bank for ths amount at 6.5% compounded monthly. She would have to pay \$150 every month to settle the loan n four years. Whch opton should she choose and why? 28. Ronald and Jll were wonderng f they should pay \$30,000 for a parkng space that was for sale n ther condomnum buldng or take a loan from the bank at 4% compounded monthly for fve years, payng monthly repayment amounts of \$460. Whch opton should they choose and why?

### Using 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 information

### 7.5. 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 information

### Section 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 information

### Simple 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 information

### Section 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 information

### Time 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 information

### Section 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 information

### Section 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 information

### Lecture 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 annuty-mmedate, and ts present value Study annuty-due, and

More information

### 8.4. 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 information

### Lecture 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 information

### EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR

EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A 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 information

### 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 information

### Level Annuities with Payments Less Frequent than Each Interest Period

Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Symoblc approach

More information

### 0.02t if 0 t 3 δ t = 0.045 if 3 < t

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

More information

### Solution: 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 information

### Texas Instruments 30Xa Calculator

Teas Instruments 30Xa Calculator Keystrokes for the TI-30Xa 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 information

### Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X 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 information

### FINANCIAL 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 information

### A 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 information

### In 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 information

### 3. 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 information

### Financial 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 information

### A) 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 information

### 1. 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 information

### Mathematics 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 information

### Time 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 information

### Thursday, 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 information

### Compound Interest: Further Topics and Applications. Chapter 9

9-2 Compound Interest: Further Topcs and Applcatons Chapter 9 9-3 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 information

### Mathematics 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 information

### Finite 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 information

### Mathematics 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 information

### In 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 information

### IDENTIFICATION 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 information

### FINANCIAL 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 information

### Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

More information

### On 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 information

### ANALYSIS 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 information

### 10.5 Future Value and Present Value of a General Annuity Due

Chapter 10 Autes 371 5. Thomas leases a car worth \$4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of \$330 each at the begg of every moth. What s the buyout prce (resdual value of the

More information

### An 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 information

### Multiple discount and forward curves

Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of

More information

### Interest 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 information

### Interest 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 (n-m) months, startng n m months: Example: Depostor wants to fx rate

More information

### In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

More information

### An 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 information

### Classic Problems at a Glance using the TVM Solver

C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the

More information

### Professor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis

Fnancal Modelng Notes Basc Excel Fnancal Functons Professor Iordans Karagannds Excel Functons Excel Functons are preformatted formulas that allow you to perform arthmetc and other operatons very quckly

More information

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

More information

### Number 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 information

### 10.3 Future Value and Present Value of an Ordinary General Annuity

360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period

More information

### Trivial 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 information

### Chapter 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 information

### Uncrystallised 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 information

### ANNUITIES. Ordinary Simple Annuities

An annuity is a series of payments or withdrawals. ANNUITIES An Annuity can be either Simple or General Simple Annuities - Compounding periods and payment periods coincide. General Annuities - Compounding

More information

### Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash

More information

### Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

### Small 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 information

### The Time Value of Money C H A P T E R N I N E

The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 \$1,000 present value \$ 10% interest \$1,464.10 future value 0 1 2 3 4 Number of periods Figure

More information

### Chapter 15 Debt and Taxes

hapter 15 Debt and Taxes 15-1. 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 information

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

More information

### Ameriprise 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 information

### Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error

Intra-year 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 information

### Staff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall

SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent

More information

### I = Prt. = P(1+i) n. A = Pe rt

11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest

More information

### Review Page 468 #1,3,5,7,9,10

MAP4C Financial Student Checklist Topic/Goal Task Prerequisite Skills Simple & Compound Interest Video Lesson Part Video Lesson Part Worksheet (pages) Present Value Goal: I will use the present value formula

More information

### Chapter 2 Applying Time Value Concepts

Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the

More information

### LIFETIME 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) 357-5200 Fax: (617) 357-5250 www.ersa-lawyers.com

More information

### Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator

More information

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

More information

### PV Tutorial Using Calculator (Sharp EL-738)

EYK 15-2 PV Tutorial Using Calculator (Sharp EL-738) TABLE OF CONTENTS Calculator Configuration and Abbreviations Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise

More information

### Continue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.

Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two

More information

### DISCLOSURES 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 information

### Effective 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 information

### Answer: 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 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

### Compounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.

Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has built-in preset assumptions

More information

### Time Value of Money. If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in

Time Value of Money Future value Present value Rates of return 1 If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.

More information

### HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR

HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that

More information

### TIME VALUE OF MONEY. Hewlett-Packard HP-12C Calculator

SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator Hewlett-Packard HP-12C Calculator CLUES, HINTS, AND TIPS Present

More information

### Effective 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 information

### The explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.

USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas

More information

### Hollinger 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 information

### Texas Instruments BAII PLUS Tutorial

To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

More information

### Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

More information

### Texas Instruments BAII PLUS Tutorial

Omar M. Al Nasser, Ph.D., MBA. Visiting Assistant Professor of Finance School of Business Administration University of Houston-Victoria Email: alnassero@uhv.edu Texas Instruments BAII PLUS Tutorial To

More information

### Chapter 3 0.06 = 3000 ( 1.015 ( 1 ) Present Value of an Annuity. Section 4 Present Value of an Annuity; Amortization

Chapter 3 Mathematcs of Face Secto 4 Preset Value of a Auty; Amortzato Preset Value of a Auty I ths secto, we wll address the problem of determg the amout that should be deposted to a accout ow at a gve

More information

### Uncrystallised 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 non-occupatonal penson scheme plan wth us, to you

More information

### Joe 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 information

### DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need \$500 one

More information

### Institute 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 information

### FINANCIAL 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 information

### 10/19/2011. Financial Mathematics. Lecture 24 Annuities. Ana NoraEvans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.

Math 40 Lecture 24 Autes Facal Mathematcs How ready do you feel for the quz o Frday: A) Brg t o B) I wll be by Frday C) I eed aother week D) I eed aother moth Aa NoraEvas 403 Kerchof AaNEvas@vrga.edu http://people.vrga.edu/~as5k/

More information

### Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes-1 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 information

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

More information

### Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

More information

### Nasdaq 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 information

### 13-2. Annuities Due. Chapter 13. MH Ryerson

13-2 Annuities Due Chapter 13 13-3 Learning Objectives After completing this chapter, you will be able to: > Calculate the future value and present value of annuities due. > Calculate the payment size,

More information

### BA II Plus Advanced Business Analyst Calculator

BA II Plus Advanced Business Analyst Calculator Quick Guide to Settings and Concepts Purpose of Guide This Quick Guide is a supplement to the BA II Plus Guidebook. It includes brief examples of commonly

More information

### TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY

TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value

More information

### Traffic-light a stress test for life insurance provisions

MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

### first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest.

ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular

More information