Chapter 5
The Time Value of Money
31. FVANn = PMT(FVIFAi,n); n = 5 years x 4 quarters/year = 20 periods
32. Amount needed in account after final deposit on your 60th birthday:
PV0 = $120,000(PVIFA.12,15) + $250,000(PVIF.12,15)
33. Present value of payments to first child for college:
$10,000 (PVIF.13,10) = $10,000 (0.295) = $2,950
Present value of payments to second child for college:
$15,000(PVIF.13,15) = $15,000(0.160) = $2,400
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Chapter 5
The Time Value of Money
Present value of retirement annuity:
Payment needed for 30 years:
34. a. PVAND0 = $100,000(PVIFA.10,20)(1 + .10)
at age 60
b. PV (at age 30) = $223,833(PVIF.12,15)
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Chapter 5
The Time Value of Money
With $10,000 available, you must save an annuity amount at the end of
each of the next 15 years that has a present value equal to $30,961, or:
35. PVAN0 = PMT(PVIFA0.10,t)
Therefore, at 10% per year his $400,000 savings will last forever, i.
36. FV7/1/2024 = $2,000 (FVIF0.07,10) + $1,000 (FVIFA0.07,6) x
37. 10% pretax x (1 – T) = 7% after tax
PVo = $15,000 (PVIF0.07,3) + $16,000 (PVIF0.07,4)
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Chapter 5
The Time Value of Money
PVAN0 = PMT (PVIFA0.07,6)
38. 10% pretax x (1 – T) = 7% after tax
PV0 = $25,000 (PVIFA0.07,4) (PVIF0.07,9)
PVAN = PMT (PVIFA0.07,10)
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Chapter 5
The Time Value of Money
Future value of $5,000 annuity at the end of year 10:
Future value of $62,889 at the end of year 30:
Net amount needed on 60th birthday:
Payment needed years 11-20:
+ PMT(FVIFA.07,5)(FVIF.09,5) + PMT(FVIFA.09,5)
PMT = $272,274 (by calculator)
End of Year Payment Interest Principal Balance
Remaining
0 — — — $1,000,000
1 $272,274 $112,500 $159,774 840,226
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Chapter 5
The Time Value of Money
*differ from $0 due to rounding.
42. Amount needed at 60th birthday = $500,000(PVIF0.07, 20)
43. Amount needed by year 35 = $200,000 (PVIFA.08,25) = $2,134,955
Future Value of amount needed from 20 year annuity payments:
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Chapter 5
The Time Value of Money
44. FVAND30 = $5,000 (FVIFA0.10,30)(1.10)
PVAN0 = PMT (PVIFA0.12,20)(1.12)
46. No recommended solution
Integrative Case Problem:
1. At age 65: n = 35; i = 0.03; PV0 = $60,000
2. At age 65: n = 15; PMT = $168,831.75 (annuity due); FV15 = $1,000,000
a. i = 0.11
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Chapter 5
The Time Value of Money
b. i = 0.06
c. i = 0.085
3. i = 0.11; FV needed = $1,556,596.62
a. At age 30: n = 35
b. At age 40: n = 25
c. At age 50: n = 15
4. i = 0.06; FV needed = $2,155,385.21
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Chapter 5
The Time Value of Money
b. At age 40: n = 25
c. At age 50: n = 15
a. At age 30: n = 35
b. At age 40: n = 25
c. At age 50: n = 15
6. The earlier one begins investing, the lower the annual payments
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