Chapter 3 ◼ The Time Value of Money (Part 1) 61
13. Present Value. Prestigious University is offering a new admission and tuition
payment plan for all alumni. On the birth of a child, parents can guarantee admission
to Prestigious University if they pay the first year’s tuition. The university will pay an
annual rate of return of 4.5% on the deposited tuition, and a full refund will be
available if the child chooses another university. The tuition is $12,000 per year at
Prestigious University and is frozen at that level for the next eighteen years. What
would parents pay today if they just gave birth to a new baby and the child will attend
college in eighteen years? How much is the required payment to secure admission for
their child if the interest rate falls to 2.5%?
14. Present Value. Standard Insurance is developing a long-life insurance policy for
people who outlive their retirement nest egg. The policy will pay out $250,000 on
your eighty-fifth birthday. You must buy the policy on your sixty-fifth birthday. The
insurance company can earn 7% on the purchase price of your policy. What is the
minimum purchase price the insurance company should charge for this policy?
15. Present Value. You are currently in the job market. Your dream is to earn a six-figure
salary ($100,000). You hope to accomplish this goal within the next thirty years. In
your field, salaries grow at 3.75% per year. What starting salary do you need to reach
this goal?
66 Brooks ◼ Financial Management: Core Concepts, 4e
a. With TVM formula (rounding to second decimal only for final answer)
b. Time Value of Money Keys or Spreadsheet inputs
Input 6.00 800.00 0 –1,609.76
Variable N I/Y PV PMT FV
Compute 12
24. Waiting period (with changing years). Jamal is waiting to be a millionaire. He wants
to know how long he must wait if
a. he invests $24,465.28 at 16% today
b. he invests $47,101.95 at 13% today
c. he invests $115,967.84 at 9% today
d. he invests $295,302.77 at 5% today
ANSWER
70 Brooks ◼ Financial Management: Core Concepts, 4e
Solutions to Advanced Problems for Spreadsheet Application
1. Future value of a portfolio. It would take 20 years to reach their $2,000,000 goal.
Growth
Rates
Money
Market
Government
Bonds
Large Cap
Small Cap
Real Estate
Portfolio Total
2.5%
5.5%
9.5%
12.0%
4.0%
Year
0
$ 37,000.00
$ 140,000.00
$ 107,000.00
$ 71,000.00
$ 87,000.00
$ 442,000.00
1
$ 37,925.00
$ 147,700.00
$ 117,165.00
$ 79,520.00
$ 90,480.00
$ 472,790.00
2
$ 38,873.13
$ 155,823.50
$ 128,295.68
$ 89,062.40
$ 94,099.20
$ 506,153.90
3
$ 39,844.95
$ 164,393.79
$ 140,483.76
$ 99,749.89
$ 97,863.17
$ 542,335.57
4
$ 40,841.08
$ 173,435.45
$ 153,829.72
$ 111,719.87
$ 101,777.69
$ 581,603.82
5
$ 41,862.10
$ 182,974.40
$ 168,443.55
$ 125,126.26
$ 105,848.80
$ 624,255.11
6
$ 42,908.66
$ 193,037.99
$ 184,445.68
$ 140,141.41
$ 110,082.75
$ 670,616.50
7
$ 43,981.37
$ 203,655.08
$ 201,968.02
$ 156,958.38
$ 114,486.06
$ 721,048.92
8
$ 45,080.91
$ 214,856.11
$ 221,154.98
$ 175,793.39
$ 119,065.51
$ 775,950.90
9
$ 46,207.93
$ 226,673.20
$ 242,164.71
$ 196,888.59
$ 123,828.13
$ 835,762.56
10
$ 47,363.13
$ 239,140.22
$ 265,170.35
$ 220,515.22
$ 128,781.25
$ 900,970.18
11
$ 48,547.21
$ 252,292.94
$ 290,361.54
$ 246,977.05
$ 133,932.50
$ 972,111.23
12
$ 49,760.89
$ 266,169.05
$ 317,945.88
$ 276,614.30
$ 139,289.80
$ 1,049,779.92
13
$ 51,004.91
$ 280,808.35
$ 348,150.74
$ 309,808.01
$ 144,861.40
$ 1,134,633.40
14
$ 52,280.03
$ 296,252.80
$ 381,225.06
$ 346,984.97
$ 150,655.85
$ 1,227,398.72
15
$ 53,587.03
$ 312,546.71
$ 417,441.45
$ 388,623.17
$ 156,682.08
$ 1,328,880.44
16
$ 54,926.71
$ 329,736.78
$ 457,098.38
$ 435,257.95
$ 162,949.37
$ 1,439,969.19
17
$ 56,299.88
$ 347,872.30
$ 500,522.73
$ 487,488.90
$ 169,467.34
$ 1,561,651.15
18
$ 57,707.37
$ 367,005.28
$ 548,072.39
$ 545,987.57
$ 176,246.04
$ 1,695,018.65
19
$ 59,150.06
$ 387,190.57
$ 600,139.26
$ 611,506.08
$ 183,295.88
$ 1,841,281.85
20
$ 60,628.81
$ 408,486.05
$ 657,152.50
$ 684,886.81
$ 190,627.71
$ 2,001,781.88
