Practice Problem 42
You invest $1,000 at a 6% annual interest rate, stated as an APR. Interest is
compounded monthly. How much will you have in 1 year? In 1.5 years?
Amount invested
APR
#
6.00%
1.00 years
1.50 years
Time period-1
Time period-2
Solution:
A
Practice Problem 41
A retiree wants level consumption in real terms over a 30-year retirement. If the
inflation rate equals the interest rate she earns on her $450,000 of savings, how
much can she spend in real terms each year over the rest of her life?
T
Practice Problem 40
The $40 million lottery payment that you just won actually pays $2 million per year for 20 years.
If the discount rate is 8% and the first payment comes in 1 year, what is the present value of the
winnings? What if the first payment co
Practice Problem 39
Youve borrowed $4,248.68 and agreed to pay back the loan with monthly payments
of $200. If the interest rate is 12% stated as an APR, how long will it take you to pay
back the loan? What is the effective annual rate on the loan?
Amount
Practice Problem 38
Consider a 4-year amortizing loan. You borrow $1,000 initially, and repay it in four equal annual
year-end payments.
a.
If the interest rate is 8%, show that the annual payment is $301.92.
b.
Fill in the following table, which shows ho
Practice Problem 36
Home loans typically involve points, which are fees charged by the lender. Each point charged
means that the borrower must pay 1% of the loan amount as a fee.
For example, if the loan is for $100,000 and 2 points are charged, the loan
Practice Problem 35
Suppose that you will receive annual payments of $10,000 for a period of 10 years. The first
payment will be made 4 years from now. If the interest rate is 5%, what is the present value
of this stream of payments?
Annual payments
Time
Practice Problem 34
a.
If you borrow $1,000 and agree to repay the loan in five equal annual payments at an interest
rate of 12%, what will your payment be?
b.
What if you make the first payment on the loan immediately instead of at the end of the first
y
Practice Problem 33
A store offers two payment plans. Under the installment plan, you pay 25% down
and 25% of the purchase price in each of the next 3 years. If you pay the entire bill
immediately, you can take a 10% discount from the purchase price. Whic
Practice Problem 32
A store offers two payment plans. Under the installment plan, you pay 25% down
and 25% of the purchase price in each of the next 3 years. If you pay the entire bill
immediately, you can take a 10% discount from the purchase price. Whic
Practice Problem 31
Your landscaping company can lease a truck for $8,000 a year (paid at year end) for 6 years.
It can instead buy the truck for $40,000. The truck will be valueless after 6 years. The interest
rate your company can earn on its funds is 7
Practice Problem 30
Your landscaping company can lease a truck for $8,000 a year (paid at year end) for 6 years.
It can instead buy the truck for $40,000. The truck will be valueless after 6 years. If the interest
rate your company can earn on its funds i
Practice Problem 30
Your landscaping company can lease a truck for $8,000 a year (paid at year end) for 6 years.
It can instead buy the truck for $40,000. The truck will be valueless after 6 years. If the interest
rate your company can earn on its funds i
Practice Problem 29
If you take out an $8,000 car loan that calls for 48 monthly payments of $240 each,
what is the APR of the loan? What is the effective annual interest rate on the loan?
What if the payments are made in four annual year-end installments
Practice Problem 28
If you take out an $8,000 car loan that calls for 48 monthly payments of $240 each, what is the APR of
the loan? What is the effective annual interest rate on the loan?
Car loan
No. of monthly payments
Monthly payment
#
48.00
$240.00
M
Practice Problem 26
In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan
is stated as $10,000 and the interest rate is 10%, the borrower pays .10 x $10,000 = $1,000
immediately, thereby receiving net funds of $
Practice Problem 25
You want to buy a new car, but you can make an initial payment of only $2,000 and can afford
monthly payments of at most $400.
a.
If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the
maximum price yo
Practice Problem 24
Professors Annuity Corp. offers a lifetime annuity to retiring professors. For a payment
of $80,000 at age 65, the firm will pay the retiring professor $600 a month until death.
a.
If the professors remaining life expectancy is 20 year
Practice Problem 23
a.
What is the present value of a 3-year annuity of $100 if the discount rate is 6%?
b.
What is the present value of the annuity in (a) if you have to wait 2 years instead
of 1 year for the first payment?
Time period(1)
Amount
Discount
Practice Problem 22
If you take out an $8,000 car loan that calls for 48 monthly payments starting after 1 month at an APR
of 10%, what is your monthly payment? What is the effective annual interest rate on the loan?
Car loan
#
No. of payments
48.00 month
Practice Problem 21
In mid-2010 a pound of apples cost $1.26, while oranges cost $1.10. Ten years earlier the price
of apples was only $.92 a pound and that of oranges was $.70 a pound. What was the annual
compound rate of growth in the price of the two f
Quiz 20
A famous quarterback just signed a $15 million contract providing $3 million a year for
5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million
now and $2 million a year for 5 years. Who is better paid? The intere
Quiz 19
A zero-coupon bond that will pay $1,000 in 10 years is selling today for $422.41.
What interest rate does the bond offer?
Face value
Time
Market Value
#
10.00
$422.41
Solution:
Interest rate =
9.00%
Quiz 17
Old Time Savings Bank pays 4% interest on its savings accounts. If you deposit
$1,000 in the bank and leave it there, how much interest will you earn in the first
year? The second year? The tenth year?
Interest rate
Deposit
Time period
Time period
Quiz 16
Investments in the stock market have increased at an average compound rate of about
5% since 1900. It is now 2012.
a.
If you invested $1,000 in the stock market in 1900, how much would that investment
be worth today?
b.
If your investment in 1900
Quiz 15
Lenny Loanshark charges 1 point per week (that is, 1% per week) on his loans. What APR
must he report to consumers? Assume exactly 52 weeks in a year. What is the effective
annual rate?
Loan Charges
Weeks in a year
1.00% per week
52.00 weeks
Solut
Quiz 14
Suppose you can borrow money at 8.6% per year (APR) compounded semiannually or 8.4% per
year (APR) compounded monthly. Which is the better deal?
APR compounded semiannually
APR compounded monthly
8.60%
8.40%
Solution:
APR
8.6%
8.4%
Compounding
per
Quiz 13
If you earn 6% per year on your bank account, how long will it take an account with $100 to
double to $200?
Interest rate
PV
FV
6.00%
$100.00
$200.00
Solution:
Time period
=
11.9 years
Quiz 12
Find the APR (the stated interest rate) for each case.
Effective Annual
Interest Rate
10.00%
6.09%
8.24%
Compounding
Period
1 month
6 month
3 month
Effective Annual
Interest Rate
10.00%
6.09%
8.24%
Compounding
Period
12 / Year
2 / Year
4 / Year
So