Section 2.3 Present Value of an Annuity; Amortization

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Section 2.3 Present Value of an Annuity; Amortization"

Transcription

1 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, every 6 months for next 3 years. r m 2 A = 1000 = PMT (perodc payment) n 1 A n n A P P A n (1.03) (1.03) (1.03) (1.03) (1.03) (1.03) 6 Years Perod P (1 ) P R n Present Value (PV) of an ordnary annuty: 1 (1 ) PV PMT n : Rate per perod n: Number of perods Notes: Payments are made at the end of each perod. 16

2 Example A car costs $,000. After a down payment of $2,000, the balance wll be pad off n 36 equal monthly payments wth nterest of 6% per year on the unpad balance, Fnd the amount of each payment. Gven: P, 000 2, , 000 n = PV PMT , 000 PMT , PMT n $13, $ / ^ (( )36) Example An annuty that earned 6.5%. A person plans to make equal annual deposts nto ths account for 25 years n order to them make 20 equal annual wthdrawals of $25,000 reducng the balance n the amount to zero. How much must be deposted annually to accumulate suffcent funds to provde for these payments? How much total nterest s earned durng ths entre 45-years process? r = annually PMT 25 k 1 25yrs 20yrs Increasng decreasng FV PV 1 (1 ) n PV PMT $275, (1.065) ^ ( ) 20 /.065 FV PV (1 ) n 1 FV PMT PMT FV PMT FV (1 ) n 1 (1.065) 25 1 $4, (1 ) n 1 Wthdraw Depost Total nterest = 20(25000) 25( ) = $

3 Amortzaton Amortzaton debt means the debt retred n gven length (= payment), Borrow money from a bank to buy and agree to payment perod (36 months) Example Borrow $5000 payment n 36 months, compounded r = %. How much payment?..01 n = 36 1 (1 ) n PV PMT PMT (1.01) 36 $ per month 5000*.01 / (1-1.01^ (-)36 )) Example If you sell your car to someone for $2,400 and agree to fnance t at 1% per month on the unpad balance, how much should you receve each month to amortze the loan n 24 months? How much nterest wll you receve? 1 (1 ) n PV PMT PMT (1.01) 24 $1.98 per month Total nterest = amount of all payment ntal loan = 24(1.98) 2400 = $ *.01/(1- (1 +.01) ^ (-)24 ) ) 18

4 Amortzaton Schedules Pay off earler last payment (lump sum) = Amortzaton schedules Example If you borrow $500 that you agree to repay n sx equal monthly payments at 1% nterest per month on the unpad balance, how much of each monthly payment s used for nterest and how much s used to reduce the unpad balance PMT $86.27 per month 1 (1.01) The end of the 1 st month nterest due = 500(.01) = $ (.01 / ( )^( ) 6 Pmt # Payment Interest Reducton Unpad Balance 0 $ $ = = $ $ (.01) = = = $ $ (.01) = = = $ $ = $ $ = $ $ = $0.0 Example Construct an amortzaton schedule for a $1,000 debt that s to be amortzed n sx equal monthly payment at 1.25% nterest rate per month on the unpad balance (1.05) 6 PMT 1000 $ per month 1 st month nterest due = 1000(.05) = $ (.05 / ( ) ^ ( ) 6 # Payment Interest Reducton Unpad Balance 0 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $0.0 $ $44.21 Total = $1000

5 Equty Equty = Current net market value Unpad balance Example A famly purchase a home 10 years ago for $80, The home was fnanced by payng 20% down for 30-year mortgage at 9%, on the unpad balance. The net market of the house s now $0, and the famly wshes to sell the house. How much equty after makng 0 monthly payments? Equty = Current Net Unpad Balance Unpad balance ( 20 ) 0 10 yrs 30 Down Payment = 20 % Left 80% =.8(80000) = 64, n = (30) = Monthly Payment? PMT PV 1 (1 ) n 64, (1.0075) ,000(.0075 / ( ) ^ ( *30) $ per month Unpad balance 10 years (now) = 20 years 1 (1 ) PV PMT n 1 (1.0075) (( ) ^ 240) / $57, Equty = current unpad balance = 0,000 57,235 = $ 62,

6 Exercses Secton 2.3 Present Value of an Annuty Amortzaton 1. How much should you depost n an account payng 8% compounded quarterly n order to receve quarterly payments of $1,000 for the next 4 years? 2. You have negotated a prce of $25,200 for a new truck. Now you must choose between 0% fnancng for 48 months or a $3,000 rebate. If you choose the rebate, you can obtan a loan for the balance at 4.5% compounded monthly for 48 months. Whch opton should you choose? 3. Suppose you have selected a new car to purchase for $19,500. If the car can be fnanced over a perod of 4 years at an annual rate of 6.9% compounded monthly, how much wll your monthly payments be? Construct an amortzaton table for the frst 3 months. 4. Suppose your parents decde to gve you $10,000 to be put n a college trust fund that wll be pad n equally quarterly nstallments over a 5 year perod. If you depost the money nto an account payng 1.5% per quarter, how much are the quarterly payments (Assume the account wll have a zero balance at the end of perod.) 5. You fnally found your dream home. It sells for $0,000 and can be purchased by payng 10% down and fnancng the balance at an annual rate of 9.6% compounded monthly. a) How much are your payments f you pay monthly for 30 years? b) Determne how much would be pad n nterest. c) Determne the payoff after 100 payments have been made. d) Change the rate to 8.4% and the tme to 15 years and calculate the payment. e) Determne how much would be pad n nterest and compare wth the prevous nterest. 6. Sharon has found the perfect car for her famly (anew mn-van) at a prce of $24,500. She wll receve a $3500 credt toward the purchase by tradng n her old Gremln, and wll fnance the balance at an annual rate of 4.8% compounded monthly. a) How much are her payments f she pays monthly for 5 years? b) How long would t take for her to pay off the car payng an extra $100 per mo., begnnng wth the frst month? 7. Mare has determned that she wll need $5000 per month n retrement over a 30-year perod. She has forecasted that her money wll earn 7.2% compounded monthly. Mare wll spend 25-years workng toward ths goal nvestng monthly at an annual rate of 7.2%. How much should Mare s monthly payments be durng her workng years n order to satsfy her retrement needs? 8. Amercan General offers a 10-year ordnary annuty wth a guaranteed rate of 6.65% compounded annually. How much should you pay for one of these annutes f you want to receve payments of $5,000 annually over the 10-year perod? 21

7 9. Amercan General offers a 7-year ordnary annuty wth a guaranteed rate of 6.35% compounded annually. How much should you pay for one of these annutes f you want to receve payments of $10,000 annually over the 7-year perod? 10. You want to purchase an automoble for $27,300. The dealer offers you 0% fnancng for 60 months or a $5,000 rebate. You can obtan 6.3% fnancal for 60 months at the local bank. Whch opton should you choose? Explan. 11. You want to purchase an automoble for $28,500. The dealer offers you 0% fnancng for 60 months or a $6,000 rebate. You can obtan 6.2% fnancal for 60 months at the local bank. Whch opton should you choose? Explan.. Construct the amortzaton schedule for a $5,000 debt that s to be amortzed n eght equal quarterly payments at 2.8% nterest per quarter on the unpad balance. 13. Construct the amortzaton schedule for a $10,000 debt that s to be amortzed n sx equal quarterly payments at 2.6% nterest per quarter on the unpad balance. 14. A loan of $37,948 wth nterest at 6.5% compounded annually, to be pad wth equal annual payments over 10 years 15. A loan of $4,836 wth nterest at 7.25% compounded sem-annually, to be repad n 5 years n equal sem-annual payments. 22

8 Secton 2.3 Present Value of an Annuty Amortzaton Exercse How much should you depost n an account payng 8% compounded quarterly n order to receve quarterly payments of $1,000 for the next 4 years? Gven: 1 1 PV PMT PMT 1, 000 r 8%.08, m 4, t 4 r n 4(4) 16 m 4 n $13, ^ 16 /.02 Exercse You have negotated a prce of $25,200 for a new truck. Now you must choose between 0% fnancng for 48 months or a $3,000 rebate. If you choose the rebate, you can obtan a loan for the balance at 4.5% compounded monthly for 48 months. Whch opton should you choose? 0% fnancng: Gven: P 25,200 r 0% 0, t 48 mth PMT 25, $525 Rebate: Gven: P 25,200 Rebate $3,000 r 4.5%.045, m n t 48 mth PV 25, 200 3, 000 $22, PMT 2 PV , 200 $ n ( / ( ^ 48)) Rebate s better and you save = $ per month Or * 48 = $ (over the loan) 22

9 Exercse Suppose you have selected a new car to purchase for $19,500. If the car can be fnanced over a perod of 4 years at an annual rate of 6.9% compounded monthly, how much wll your monthly payments be? Construct an amortzaton table for the frst 3 months / PMT ( / ) 48 I 19500(0.069 / ) (0.069 / ) / (1 ( / ) ^ 48 Pmt # Pmt Amount Interest Reducton Unpad Bal Exercse Suppose your parents decde to gve you $10,000 to be put n a college trust fund that wll be pad n equally quarterly nstallments over a 5 year perod. If you depost the money nto an account payng 1.5% per quarter, how much are the quarterly payments (Assume the account wll have a zero balance at the end of perod.) Gven: PV 10, 000 r 1.5%.015, m 4, t 5 r.015 n 4(5) PMT 10, 000 $ ( ) (0.015) / (1 ( ) ^ 20) 23

10 Exercse You fnally found your dream home. It sells for $0,000 and can be purchased by payng 10% down and fnancng the balance at an annual rate of 9.6% compounded monthly. a) How much are your payments f you pay monthly for 30 years? b) Determne how much would be pad n nterest. c) Determne the payoff after 100 payments have been made. d) Change the rate to 8.4% and the tme to 15 years and calculate the payment. e) Determne how much would be pad n nterest and compare wth the prevous nterest. a) / PMT $ ( / ) b) I 360(916.01) $ c) PV ( / ) $ / d) PMT / $ ( / ) e) I 180( ) $ I1 I Exercse Sharon has found the perfect car for her famly (anew mn-van) at a prce of $24,500. She wll receve a $3500 credt toward the purchase by tradng n her old Gremln, and wll fnance the balance at an annual rate of 4.8% compounded monthly. a) How much are her payments f she pays monthly for 5 years? b) How long would t take for her to pay off the car payng an extra $100 per mo., begnnng wth the frst month? a) b) / PMT $ ( / ) n 1 ( / ) / Dvde both sdes by

11 1 ( ) n n n multply by n ln both sdes n ln1.004 ln n ln / ln ln n 47 mo. n ln1.004 Money s compounded monthly; t can t be compounded at months. Bump to 47mo. Exercse Mare has determned that she wll need $5000 per month n retrement over a 30-year perod. She has forecasted that her money wll earn 7.2% compounded monthly. Mare wll spend 25-years workng toward ths goal nvestng monthly at an annual rate of 7.2%. How much should Mare s monthly payments be durng her workng years n order to satsfy her retrement needs? Ths s a 2-part problem: 1 st calculate the PV for retrement. Then use that value as FV for workng years ( / ) PV / Exercse Amercan General offers a 10-year ordnary annuty wth a guaranteed rate of 6.65% compounded annually. How much should you pay for one of these annutes f you want to receve payments of $5,000 annually over the 10-year perod? Gven: PMT 5, 000 r 6.65%.0665, m 1, t 10 r.0665 n 1(10) 10 m n 11 PV PMT 1 ( ) 5, $35, (1.0665) ^ 10 /.0665

12 Exercse Amercan General offers a 7-year ordnary annuty wth a guaranteed rate of 6.35% compounded annually. How much should you pay for one of these annutes f you want to receve payments of $10,000 annually over the 7-year perod? Gven: PMT 10,000 r 6.35%.0635, m 1, t 7 r.0635 n 7 m 1 1 PV PMT n 1 ( ) 7 10, $55, (1.0635) ^ 7 /.0635 Exercse You want to purchase an automoble for $27,300. The dealer offers you 0% fnancng for 60 months or a $5,000 rebate. You can obtan 6.3% fnancal for 60 months at the local bank. Whch opton should you choose? Explan. 0% fnancng: Gven: Rebate: Gven: 27, 300 PMT 1 60 P 27,300 r 0% 0, t 60 mo $ Rebate $5, 000 r 6.3%.063, n 60 PV 27, 300 5, 000 $22, PMT 2 PV , $ n ( / ( / ^ 60)) Rebate s better and you save $455 $ $20.76 per month Or $1, (over the lfe of the loan) 26

13 Exercse You want to purchase an automoble for $28,500. The dealer offers you 0% fnancng for 60 months or a $6,000 rebate. You can obtan 6.2% fnancal for 60 months at the local bank. Whch opton should you choose? Explan. 0% fnancng: Gven: P 28,500 r 0% 0, t 60 mo Rebate: Gven: 28, 500 PMT 1 60 $ Rebate $6, 000 r 6.2%.062, n 60 PV 28, 500 6, 000 $22, PMT 2 PV , $ n Rebate s better and you save $475 $ $37.92 per month Or $2, (over the lfe of the loan) Exercse Construct the amortzaton schedule for a $5,000 debt that s to be amortzed n eght equal quarterly payments at 2.8% nterest per quarter on the unpad balance. Gven: PV 5,000 r 2.8%.028, n 8 PMT PV 1 1 n 5, $ (.028 / ( ^ 8)) 27

14 Pmt Payment Interest Reducton Unpad Balance # 0 $0 $5, $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Total $5, $ $5, $4, $3, $3, $2, $2, $1, $ $0.00 Exercse Construct the amortzaton schedule for a $10,000 debt that s to be amortzed n sx equal quarterly payments at 2.6% nterest per quarter on the unpad balance. Gven: PV 10,000 r 2.6%.026, n 6 PMT PV 1 1 n 10, $1, (.026 / ( ^ 6)) Pmt # Payment Interest Reducton Unpad Balance 0 $0 $10, $1, $ $1, $8, $1, $1, $1, $1, $ $ $ $ $1, $ $1, $6, $1, $5, $1, $3, $1, $1, Total $10, $ $10, $1, $

15 Exercse A loan of $37,948 wth nterest at 6.5% compounded annually, to be pad wth equal annual payments over 10 years Gven: PV 37,948. m 1, r 6.5%.065, n 10 PMT PV 1 1 n 37, $5, (.065 / ( ^ 10)) Pmt # Payment Interest Reducton Unpad Balance 0 $37, $5, $2, $2,8. $35, $5, $2, $2, $32, $5, $2, $3, $28, $5, $1, $3, $25, $5, $1, $3, $21, $5, $1, $3, $18, $5, $1, $4, $13, $5, $ $4, $9, $5, $ $4, $4, $5, $ $4, $0.00 Total $52, $14, $37,

16 Exercse A loan of $4,836 wth nterest at 7.25% compounded sem-annually, to be repad n 5 years n equal semannual payments. Gven: PV 4,836. m 2, r 7.25%.0725, t 5 r n 2 5 m 2 10 PMT PV 1 1 n 4, $ ( / ( ^ 10)) Pmt # Payment Interest Reducton Unpad Balance 0 $4, $ $ $ $4, $ $ $ $4, $ $ $ $3, $ $9.10 $ $3, $ $1.57 $ $2, $ $95.43 $ $2, $ $77.68 $ $1, $ $59.29 $ $1, $ $40.22 $ $ $ $20.47 $ $0.00 Total $5, $1, $4,

Section 2.2 Future Value of an Annuity

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

Using Series to Analyze Financial Situations: Present Value

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

10.2 Future Value and Present Value of an Ordinary Simple Annuity

10.2 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 information

Simple Interest Loans (Section 5.1) :

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

7.5. Present Value of an Annuity. Investigate

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

Finite Math Chapter 10: Study Guide and Solution to Problems

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

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

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

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.

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

Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.

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

Section 5.4 Annuities, Present Value, and Amortization

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

1. Math 210 Finite Mathematics

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

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

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

Thursday, December 10, 2009 Noon - 1:50 pm Faraday 143

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

0.02t if 0 t 3 δ t = 0.045 if 3 < t

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

FINANCIAL MATHEMATICS

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

8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value

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

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

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

Section 5.3 Annuities, Future Value, and Sinking Funds

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

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

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

A) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.

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

Mathematics of Finance

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

Lecture 3: Force of Interest, Real Interest Rate, Annuity

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

3. Present value of Annuity Problems

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

Texas Instruments 30Xa Calculator

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 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

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

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

Level Annuities with Payments Less Frequent than Each Interest Period

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

Compound Interest: Further Topics and Applications. Chapter 9

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

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

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

EXAMPLE PROBLEMS SOLVED USING THE SHARP EL-733A CALCULATOR

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

Mathematics of Finance

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

A Master Time Value of Money Formula. Floyd Vest

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

Interest Rate Futures

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

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals

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

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

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 Mathemetics

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

On some special nonlevel annuities and yield rates for annuities

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 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

Chapter 15 Debt and Taxes

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

Effective December 2015

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

Effective September 2015

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

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value. Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

More information

Compounding Quarterly, Monthly, and Daily

Compounding Quarterly, Monthly, and Daily 126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

More information

FINANCIAL MATHEMATICS 12 MARCH 2014

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

An Alternative Way to Measure Private Equity Performance

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

Small pots lump sum payment instruction

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

Trivial lump sum R5.0

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

Uncrystallised funds pension lump sum payment instruction

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

Joe Pimbley, unpublished, 2005. Yield Curve Calculations

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

Chapter 4: Time Value of Money

Chapter 4: Time Value of Money FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)

More information

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26 Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.

More information

Chapter 4 Financial Markets

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

AS 2553a Mathematics of finance

AS 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 information

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest! TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on

More information

10.5 Future Value and Present Value of a General Annuity Due

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

Professor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis

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

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

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

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )

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

Discounted Cash Flow Valuation

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

Stock Profit Patterns

Stock Profit Patterns Stock Proft Patterns Suppose a share of Farsta Shppng stock n January 004 s prce n the market to 56. Assume that a September call opton at exercse prce 50 costs 8. A September put opton at exercse prce

More information

An Overview of Financial Mathematics

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

Problem Set: Annuities and Perpetuities (Solutions Below)

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

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved. 2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical defined-contribution

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

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

DISCLOSURES I. ELECTRONIC FUND TRANSFER DISCLOSURE (REGULATION E)... 2 ELECTRONIC DISCLOSURE AND ELECTRONIC SIGNATURE CONSENT... 7

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

Example. L.N. Stout () Problems on annuities 1 / 14

Example. L.N. Stout () Problems on annuities 1 / 14 Example A credit card charges an annual rate of 14% compounded monthly. This month s bill is $6000. The minimum payment is $5. Suppose I keep paying $5 each month. How long will it take to pay off the

More information

CHAPTER 2. Time Value of Money 6-1

CHAPTER 2. Time Value of Money 6-1 CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show

More information

HOW TO CALCULATE PRESENT VALUES

HOW TO CALCULATE PRESENT VALUES Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

More information

Account Transfer and Direct Rollover

Account 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 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 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

The Time Value of Money

The Time Value of Money The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future

More information

Classic Problems at a Glance using the TVM Solver

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

LIFETIME INCOME OPTIONS

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

FIN 3000. Chapter 6. Annuities. Liuren Wu

FIN 3000. Chapter 6. Annuities. Liuren Wu FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate

More information

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

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

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years. 6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in

More information

Ameriprise Financial Services, Inc. or RiverSource Life Insurance Company Account Registration

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

FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1

FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 FIN 5413: Chapter 03 - Mortgage Loan Foundations: The Time Value of Money Page 1 Solutions to Problems - Chapter 3 Mortgage Loan Foundations: The Time Value of Money Problem 3-1 a) Future Value = FV(n,i,PV,PMT)

More information

Chapter F: Finance. Section F.1-F.4

Chapter F: Finance. Section F.1-F.4 Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given

More information

Activity 3.1 Annuities & Installment Payments

Activity 3.1 Annuities & Installment Payments Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.

More information

Loans Practice. Math 107 Worksheet #23

Loans Practice. Math 107 Worksheet #23 Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following,

More information

Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =

Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R = Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are

More information

Bond futures. Bond futures contracts are futures contracts that allow investor to buy in the

Bond 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 information

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

More information

Nasdaq Iceland Bond Indices 01 April 2015

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

MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the

More information

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

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

FINANCIAL CALCULATIONS

FINANCIAL CALCULATIONS FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N

More information

2. How many months will it take to pay off a $9,000 loan with monthly payments of $225? The APR is 18%.

2. How many months will it take to pay off a $9,000 loan with monthly payments of $225? The APR is 18%. Lesson 1: The Time Value of Money Study Questions 1. Your mother, who gave you life (and therefore everything), has encouraged you to borrow $65,000 in student loans. The interest rate is a record-low

More information

Midterm 1 Practice Problems

Midterm 1 Practice Problems Midterm 1 Practice Problems 1. Calculate the present value of each cashflow using a discount rate of 7%. Which do you most prefer most? Show and explain all supporting calculations! Cashflow A: receive

More information

Present Value and Annuities. Chapter 3 Cont d

Present Value and Annuities. Chapter 3 Cont d Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects

More information

The Time Value of Money

The Time Value of Money The Tme Value of Moey 1 Iversemet Optos Year: 1624 Property Traded: Mahatta Islad Prce : $24.00, FV of $24 @ 6%: FV = $24 (1+0.06) 388 = $158.08 bllo Opto 1 0 1 2 3 4 5 t ($519.37) 0 0 0 0 $1,000 Opto

More information

Time Value of Money. (1) Calculate future value or present value or annuity? (2) Future value = PV * (1+ i) n

Time Value of Money. (1) Calculate future value or present value or annuity? (2) Future value = PV * (1+ i) n Problem 1 Happy Harry has just bought a scratch lottery tcket ad wo 10,000. He wats to face the future study of hs ewly bor daughter ad vests ths moey a fud wth a maturty of 18 years offerg a promsg yearly

More information

Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.

Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr. Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated

More information

How to calculate present values

How to calculate present values How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

More information

Properties of American Derivative Securities

Properties 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 non-negatve random varables fg k g n k= suc tat eac G k s F k -measurable. Te owner

More information

Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start

More information