CFIN4
Chapter 4 – Time Value of Money
87. Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. He wants a
retirement income which has, in the first year, the same purchasing power as $40,000 has today. However, his
retirement income will be of a fixed amount, so his real income will decline over time. His retirement income will
start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected
to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and
in the future. How much must he save each year, starting today, to meet his retirement goals?
a. $1,863
b. $2,034
c. $2,716
d. $5,350
e. $6,102
88. Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. Suppose your
father wants to have a real income of $40,000 in today’s dollars in each year after he retires. His retirement income
will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is
expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on
savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a. $1,863
b. $2,034
c. $2,716
d. $5,350
e. $6,102
89. Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today
her retirement and is establishing a retirement account with your office. She would like to withdraw money from her
retirement account on her birthday each year until she dies. She would ideally like to withdraw $50,000 on her 85th
birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw
$73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave $200,000 to
her descendants. Your client currently has $100,000. You estimate that the money in the retirement account will earn
percent a year over the next 15 years. Your client plans to contribute an equal amount of money each year until her
retirement. Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her
85th birthday). How much should she contribute each year in order to meet her objectives?
a. $12,401.59
b. $12,998.63
c. $13,243.18
d. $13,759.44
e. $14,021.53
90. You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the
first three years. The security will then pay $30 a year at the end of each of the next 20 years. The simple interest
rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this
information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?
a. $35
b. $38
c. $40
d. $45
e. $50
CFIN4
Chapter 4 – Time Value of Money
91. You are currently saving for your child‘s college education. The current cost of college is $10,000 a year. You expect
that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a
four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currentl
have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by
the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the
next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0
and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your
child‘s education?
a. $1,133.16
b. $1,393.42
c. $1,477.02
d. $1,507.81
e. $1,622.33
CFIN4
Chapter 4 – Time Value of Money
92. You will receive a $100 annual perpetuity, the first payment to be received now, at Year 0, a $300 annual perpetuity
payable starting at the end of Year 5, and a $200 semiannual (2 payments per year) perpetuity payable starting midw
through Year 10. If you require an effective annual interest rate of 14.49 percent, what is the present value of all thr
perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)
a. $2,091.86
b. $2,785.14
c. $4,213.51
d. Infinite; the present value of any perpetuity is infinite.
e. Cannot determine the value since some payments are annually and some semiannually.
93. Hillary is trying to determine the cost of health care to college students, and parents’ ability to cover those costs. She
assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18
when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that
parents can save $100 per year to help cover their children’s costs. All payments occur at the end of the relevant
period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings
can be invested at a simple rate of 6 percent, annual compounding. Hillary wants a health care plan which covers the
fully inflated cost of health care for a student for 4 years, during years 19 through 22 (with payments made at the end
of years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement
the average parent‘s share of a child‘s college health care cost? The lump sum the government sets aside will also be
invested at 6 percent, annual compounding.
a. $1,082.76
b. $3,997.81
c. $5,674.23
d. $7,472.08
e. $8,554.84
94. You have some money on deposit in a bank account which pays a simple (or quoted) rate of 8.0944 percent, but with
interest compounded daily (using a 365-day year). Your friend owns a security which calls for the payment of
$10,000 after 27 months. The security is just as safe as your bank deposit, and your friend offers to sell it to you for
$8,000. If you buy the security, by how much will the effective annual rate of return on your investment change?
a. 1.87%
b. 1.53%
c. 2.00%
d. 0.96%
e. 0.44%
95. Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early
retirement. The first payment will be made 3 months from now. At the end of 20 years (80 payments), you will be pa
10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20). Th
funds will be invested at a simple rate of 8.0 percent, quarterly compounding, during both the accumulation and the
distribution periods. How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of
your calculations.)
a. $7,561
b. $10,789
c. $11,678
d. $12,342
e. $13,119