Finance Answers

Today is his 24th birthday. He plans to retire at 65 years old and he expects to live for another 20 years afterwards. He wants an income of $30,000 per year during his retirement years, to be paid annually on his birthday (starting from his 65th birthday). He plans to save some amount at each birthday from the age 25 to 64. He thinks about saving a constant amount for the first 10 years and then increases his saving at 3% each year until the last one before his retirement. The bank provides two types of accounts. One account pays 6.9%/year compounded quarterly. The other account pays 7%/year compounded annually?
(a) What is the balance of your brother’s account right after he makes his deposit in
his saving account on his 50th birthday?

Today is his 24th birthday. He plans to retire at 65 years old and he expects to live for another 20 years afterwards. He wants an income of $30,000 per year during his retirement years, to be paid annually on his birthday (starting from his 65th birthday). He plans to save some amount at each birthday from the age 25 to 64. He thinks about saving a constant amount for the first 10 years and then increases his saving at 3% each year until the last one before his retirement. The bank provides two types of accounts. One account pays 6.9%/year compounded quarterly. The other account pays 7%/year compounded annually?
(a) Which account would you recommend? Why?
(b) After choosing the proper account, how much should your brother save each year
for the first 10 years?
(c) What is the balance of your brother’s account right after he makes his deposit in
his saving account on his 50th birthday?

Suppose there are two investors: A and B. Both plan to retire after T years but save for their
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.

The yields to maturity on five zero coupon bonds are given below:
Years to Maturity: 1 year (yield of 12%), 2 years (yield of 14%), 3 years (yield of 15%), 4 years (yield of 15.5%), and 5 years (yield of 15.7%)
(a)What is the implied forward rate for the third year?
(b) Compute the yield to maturity of a 5-year annual coupon bond with a coupon
rate of 5%. Also compute the yield to maturity of a 5-year annual coupon bond
with a coupon rate of 10%. Which one is higher, why?

Suppose there are two investors: A and B. Both plan to retire after T years but save for their
retirement in very different ways. Investor A puts $1 into his retirement account at
the beginning of each year for T years (i.e., at t = 0, 1, . . . , T − 1). Investor B does
not make any contributions for the first N years, and try to make it up with more
contributions at the start of each year for the remaining T −N years, i.e., he will make
contributions at t = N, N + 1, . . . , T − 1.
(a) Suppose Investor B wants to have the same amount of money as Investor A when
both of them retire. What is the annual contribution that Investor B has to make
in the remaining T − N years. Express your answer as a function of r, N and T.
(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that
Investor B has to make in part (a) as a function of N for 0 ≤ N ≤ 40 years.
Repeat the same exercise for r = 0.04/year and r = 0.06/year.

• A coupon bond with a coupon rate of 8% and a face value of $1,000. Coupons
are paid out annually and the bond has 1 year to maturity. The current coupon
has just been paid out. The current price of the bond is $1018.772.
• A zero coupon bond with a face value of $1,000 and 2 years to maturity. The
bond trades at $907.029.
• An annuity that pays $50 every year for the next 3 years. The next payment will
be a year from now and the last payment will be 3 years from now. The annuity
is currently worth $136.967.
All these securities are risk-free. Note that there is no direct borrowing and lending
here, so if you want to borrow (lend) you need to sell (buy) an appropriate bond.
(a) Find the term structure of spot interest rates (i.e., r1, r2 and r3: rates for the
next 1, 2, and 3 years).
(b) Find the term structure of forward interest rates (i.e., rates between years 0 and
1, between years 1 and 2, and between years 2 and 3).

Thelma and Louie, Inc., started the year with a balance of retained earnings of $550 million and ended the year with retained earnings of $600 million. The company paid dividends of $40 million to the preferred stockholders and $80 million to common stockholders.

Calculate Thelma and Louie’s net income for the year. (Enter your answer in millions of dollars.)

Net income $

If the corporate tax rate were to decrease, from a purely WACC perspective, what would a business want to do?

You went shopping a month ago, racking charges of $2,000 to your credit card along
the way. Then the credit card statement comes, and it says your minimum monthly
payment is only $40. Suppose you only pay the minimum payment of $40 every month.
If the stated interest rate is 24%/year, compounded monthly, how long does it take for
you to pay off your credit card debt? For simplicity, assume the first payment is due
immediately, and your credit card company starts charging you interest after the first
day of the first payment.

When must you sign a deposit slip?
a.
You must always sign a deposit slip.
b.
You only need to sign a deposit slip when receiving cash.
c.
You only need to sign a deposit slip when using an ATM, rather than depositing at the bank.
d.
You never need to sign a deposit slip. Your account information is enough.