This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Solutions to Chapter 5 The Time Value of Money 1. a. $100/(1.08) 10 = $46.32 b. $100/(1.08) 20 = $21.45 c. $100/(1.04) 10 = $67.56 d. $100/(1.04) 20 = $45.64 2. a. $100 × (1.08) 10 = $215.89 b. $100 × (1.08) 20 = $466.10 c. $100 × (1.04) 10 = $148.02 d. $100 × (1.04) 20 = $219.11 3. $100 × (1.04) 113 = $8,409.45 $100 × (1.08) 113 = $598,252.29 4. With simple interest, you earn 4% of $1,000 or $40 each year. There is no interest on interest. After 10 years, you earn total interest of $400, and your account accumulates to $1,400. With compound interest, your account grows to: $1,000 × (1.04) 10 = $1480.24 Therefore $80.24 is interest on interest. 5. PV = $700/(1.05) 5 = $548.47 51 6. Present Value Years Future Value Interest Rate a. $400 11 $684 % 00 . 5 1 400 684 ) 11 / 1 ( = b. $183 4 $249 % 00 . 8 1 183 249 ) 4 / 1 ( = c. $300 7 $300 % 1 300 300 ) 7 / 1 ( = To find the interest rate, we rearrange the basic future value equation as follows: FV = PV × (1 + r) t ⇒ r = 1 PV FV ) t / 1 ( 7. You should compare the present values of the two annuities. a. 73 . 721 , 7 $ (1.05) 0.05 1 0.05 1 $1,000 PV 10 = × × = 73 . 303 , 8 $ (1.05) 0.05 1 0.05 1 $800 PV 15 = × × = b. 47 . 192 , 4 $ (1.20) 0.20 1 0.20 1 $1,000 PV 10 = × × = 38 . 740 , 3 $ (1.20) 0.20 1 0.20 1 $800 PV 15 = × × = c. When the interest rate is low, as in part (a), the longer (i.e., 15year) but smaller annuity is more valuable because the impact of discounting on the present value of future payments is less significant. 8. $100 × (1 + r) 3 = $115.76 ⇒ r = 5.00% $200 × (1 + r) 4 = $262.16 ⇒ r = 7.00% $100 × (1 + r) 5 = $110.41 ⇒ r = 2.00% 52 9. PV = ($200/1.06) + ($400/1.06 2 ) + ($300/1.06 3 ) = $188.68 + $356.00 + $251.89 = $796.57 10. In these problems, you can either solve the equation provided directly, or you can use your financial calculator, setting: PV = ( )400, FV = 1000, PMT = 0, i as specified by the problem. Then compute n on the calculator. a. $400 × (1.04) t = $1,000 ⇒ t = 23.36 periods b. $400 × (1.08) t = $1,000 ⇒ t = 11.91 periods c. $400 × (1.16) t = $1,000 ⇒ t = 6.17 periods 11. APR Compounding period Effective annual rate a. 12% 1 month (m = 12/yr) 1.01 12 1 = 0.1268 = 12.68% b. 8% 3 months (m = 4/yr) 1.02 4 1 = 0.0824 = 8.24% c. 10% 6 months (m = 2/yr) 1.05 2 1 = 0.1025 = 10.25% 12. Effective R at e Compounding period Per period rate APR a. 10.00% 1 month (m = 12/yr) 1.10 (1/ 12) 1 = 0.0080 0.096 = 9.6% b. 6.09% 6 months (m = 2/yr) 1.0609 (1/ 2) 1 = 0.0300 0.060 = 6.0% c. 8.24% 3 months (m = 4/yr) 1.0824 (1/ 4) 1 = 0.0200 0.080 = 8.0% 13. Solve the following for t: 1.08 t = 2 ⇒ t = 11.9 years 53 On a financial calculator, enter: PV = ( )1, FV = 2, PMT = 0, i = 6 and then compute n....
View
Full
Document
This note was uploaded on 01/18/2012 for the course FIN 254 taught by Professor Gingerwagner during the Fall '11 term at Syracuse.
 Fall '11
 GingerWagner
 Time Value Of Money, Corporate Finance

Click to edit the document details