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115.
You want to be a millionaire when you retire in 40 years. You can earn A
12.5 percent annual return. How much more will you have to save each
month if you wait 10 years to start saving versus if you start saving at the
end of this month?
116.
You have just won the lottery and will receive $540,000 as your first
payment one year from now. You will receive payments for 26 years. The
payments will increase in value by 4 percent each year. The appropriate
discount rate is 10 percent. What is the present value of your winnings?
117.
You are preparing to make monthly payments of $72, beginning at the end
of this month, into an account that pays 6 percent interest compounded
monthly. How many payments will you have made when your account
balance reaches $9,312?
118.
You want to borrow $47,170 from your local bank to buy a new sailboat. You
can afford to make monthly payments of $1,160, but no more. Assume
monthly compounding. What is the highest rate you can afford on a 48-
month APR loan?
119.
You need a 30-year, fixed-rate mortgage to buy a new home for $240,000.
Your mortgage bank will lend you the money at a 7.5 percent APR for this
360-month loan, with interest compounded monthly. However, you can only
afford monthly payments of $850, so you offer to pay off any remaining loan
balance at the end of the loan in the form of a single balloon payment. What
will be the amount of the balloon payment if you are to keep your monthly
payments at $850?
120.
The present value of the following cash flow stream is $5,933.86 when
discounted at 11 percent annually. What is the value of the missing cash
flow?
121.
You have just purchased a new warehouse. To finance the purchase, you've
arranged for a 30-year mortgage loan for 80 percent of the $2,600,000
purchase price. The monthly payment on this loan will be $12,200. What is
the effective annual rate on this loan?
122.
Consider a firm with a contract to sell an asset 3 years from now for
$90,000. The asset costs $71,000 to produce today. At what rate will the
firm just break even on this contract?
123.
What is the present value of $1,100 per year, at a discount rate of 10
percent if the first payment is received 6 years from now and the last
payment is received 30 years from now?
124.
You have your choice of two investment accounts. Investment A is a 5-year
annuity that features end-of-month $2,500 payments and has an interest
rate of 11.5 percent compounded monthly. Investment B is a 10.5 percent
continuously compounded lump sum investment, also good for five years.
How much would you need to invest in B today for it to be worth as much as
investment A five years from now?
125.
Given an interest rate of 8 percent per year, what is the value at date t = 9
of a perpetual stream of $500 annual payments that begins at date t = 17?
126.
You want to buy a new sports car for $55,000. The contract is in the form of
a 60-month annuity due at a 6 percent APR, compounded monthly. What
will your monthly payment be?
127.
You are looking at a one-year loan of $10,000. The interest rate is quoted as
8 percent plus 5 points. A point on a loan is simply 1 percent (one
percentage point) of the loan amount. Quotes similar to this one are very
common with home mortgages. The interest rate quotation in this example
requires the borrower to pay 5 points to the lender up front and repay the
loan later with 10 percent interest. What is the actual rate you are paying on
this loan?
128.
Your holiday ski vacation was great, but it unfortunately ran a bit over
budget. All is not lost. You just received an offer in the mail to transfer your
$5,000 balance from your current credit card, which charges an annual rate
of 18.7 percent, to a new credit card charging a rate of 9.4 percent. You plan
to make payments of $510 a month on this debt. How many less payments
will you have to make to pay off this debt if you transfer the balance to the
new card?
Essay Questions
129.
Explain the difference between the effective annual rate (EAR) and the
annual percentage rate (APR). Of the two, which one has the greater
importance and why?
130.
You are considering two annuities, both of which pay a total of $20,000 over
the life of the annuity. Annuity A pays $2,000 at the end of each year for the
next 10 years. Annuity B pays $1,000 at the end of each year for the next 20
years. Which annuity has the greater value today? Is there any circumstance
where the two annuities would have equal values as of today? Explain.
131.
Why might a borrower select an interest-only loan instead of an amortized
loan, which would be cheaper?
132.
Kristie owns a perpetuity which pays $12,000 at the end of each year. She
comes to you and offers to sell you all of the payments to be received after
the 10th year. Explain how you can determine the value of this offer.
