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Chapter 4 time value of money

Chapter 4: Problems (from p. 180): 4-5, 4-7, 4-8, 4-9, 4-11, 4-12, 4-13, 4-15, 419, 4-20, 4-25, 4-26, 4-30, 4-31
Suppose you make an investment of $1,000 now. This first year the investment
returns 12%, the second year it returns 6%, and the third year it returns 8%. How
much would this investment be worth at the end of the third year, assuming no
withdrawals are made in between?
A wealthy relative gives Barney $5,000 to help provide for his new born child’s
university fee. He decides to invest this money at 10% p.a. until his child is ready to go
to university. How much will be in the account 18 years from now?
Barney wants to provide $20,000 for his new born child’s education, which will
begin 18 years from today. How much should Barney invest now, if the interest rate is
10% p.a.

Barney lends $100,000 to John, his cousin for a total of 10 years at 5% p.a.

How much does John have to pay after 10 years (if using simple interest

How much does John have to pay after 10 years (if using compounded
interest rate)?
Assume that Barney lends $100,000 to John, using simple interest rate,
but wants to receive the payment which is equal to that if using compounded interest.
What should the interest rate be?
How long will it take for a $1,000 investment to double in size when invested at
the rate of 8% per year?
How long will it take for a $3,000 investment to grow to $10,000 if invested at 5%

compounded annually?


compounded quarterly?

You borrow money on your credit card at 17.5% p.a., compounding quarterly.
What is the effective annual interest rate?

The following interest rates are being offered by three competing banks: 4%
compounded monthly; 4.1% compounded quarterly; 4.15% compounded annually.
Which one is the most attractive?
On a contract, you have a choice of receiving $25,000 six years from now or
$50,000 twelve years from now. At what implied compound annual interest rate should
you be indifferent between the two contracts?
You have just won the prize in the State lottery. A recent innovation is to offer
prize winners a choice of payoffs. You must choose one of the following prizes:

$1,000,000 paid immediately

$600,000 paid exactly one year from today, and another
exactly 3 years from today

$600,000 paid

$70,000 payment at the end of each year forever (first payment occurs
exactly 1 year from today)
An immediate payment of $600,000, then beginning exactly 5 years from
today, an annual payment of $50,000 forever
An annual payment of $200,000 for the next 7 years (first payment occurs
exactly 1 year from today)
You believe that 8% p.a. compounded annually is an appropriate discount rate.
Assuming you wish to maximize your current wealth, which is the best prize?
Your company anticipates the introduction of environmental protection laws 3
years from now. Under these laws, you will have to pay an environment tax of $5,000 at
the end of each year. If the rate is 6% p.a., what is the present value of your company’s
obligation under this law?
Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will
provide him with a steady income over the next 12 years. He has heard that the local
bank is currently paying 6% p.a. (compounding annually). If he were to deposit his fund,
what is the equal amount would he be able to withdraw at the end of each year for 12
After graduation, you plan to work for your local bank for 12 years and then start
your own business. You expect to save and deposit $7,500 a year for the first 6 years
and $15,000 annually for the following 6 years. The first deposit will be made a year
from today. In addition, your grandfather just gave you a $25,000 graduation gift which

you will deposit immediately. If the account earns 9% compounded annually, how much
will you have when you start your business 12 years from now?
Muffin Megabucks is considering two different savings plans in 10 years. The first
plan would have her deposit $500 every six months, and she would receive an interest
rate at 7% p.a. (compounding semi-annually). Under the second plan she could deposit
$1,000 every year with the rate of interest of 7.5% p.a. (compounding annually). Which
plan should Muffin use? (Assuming that the initial deposit of Plan 1 would be made 6
months from now, and with Plan 2, one year from now).
Kate’s financial advisor tells her that she will need $2 million to fund her
retirement. She plans to work for another 30 years before retiring. She will make 30
contributions to a pension plan. How much will each contribution be, if the interest rate
is 9% p.a.?
Mary has just retired and has $1 million in her retirement account. Her bank
offers an arrangement whereby the bank takes her $1 million now and pays her
$110,000 at the end of each year for the next 20 years. Is it a fair deal, if the offered rate
is 10% p.a.?
Mr. Doody, at age 70, is expected to live for 15 years. If he can invest at 12% per
annum compounded monthly, how much does he need now to guarantee himself $300
every month for the next 15 years?
Daryl wishes to save money to provide for his retirement. Beginning one month
from now, he will deposit a fixed amount into a retirement savings account that will earn
12% p.a. compounded monthly for 30 years. Then, one year after making his final
deposit, he will withdraw $100,000 annually for 25 years. How much should Daryl
deposit for the first 30 years to meet his objective if the fund earns the interest rate of
12.68% p.a., compounded annually during the last 25 years?
The Happy Hang Glide Company is purchasing a building and has obtained a
$190,000 mortgage loan for 20 years. The loan bears a compound interest rate of 17%
p.a. and calls for equal annual installment payments at the end of each of 20 years.
What is the amount of annual payment?
A home buyer is purchasing a $140,000 house. The down payment will be 20%
of the price of the house, and the remainder will be financed by a 30-year mortgage at a
rate of 9.8% interest compounded monthly. What will the monthly payment be?
Compare the monthly payments and the total amounts of interest paid if a 15-year
mortgage is chosen instead of a 30-year mortgage.

Ann obtains a $150,000, 20-year mortgage with a bank at 9% p.a., compounded

What is her monthly repayment?

Suppose that after 5 years, Ann plans to repay the loan by making an
additional payment each month along with her regular payment. How much must Ann
pay each month if she wishes to pay off the loan in 10 years?
Mark wants to buy a new car for his wife and agrees with a 1.5-year, $12,000
loan. The financial institution quotes this loan at 10.5%, compounded monthly. Six
months later, Mark is offered an optional loan from another financial institution. The new
loan is quoted at 9.25% and Mark asks that the number of payments be set to 12. A 1%
fee will be added to the remaining loan balance for the principal of the new loan. What
was the first loan monthly payment and what is the amount Mark is going to pay for the
new one? Is it a good idea to change?
Mary enters into a loan agreement to borrow $90,000 to help finance the
purchase of her new home.
The agreement specifies the term of 20 years with monthly repayment at
the fixed rate of 9% p.a. (compounded monthly). What is her monthly payment?
Five years has passed. A rival lender offers to refinance Mary’s loan at the
fixed rate of 8% p.a. (compounded monthly). The cost associated with this refinancing is
$1,500. Should she refinance?
Suppose 9 years have passed since Mary enters the original loan. She’s
considering making an extra payment of $10,000 off her loan. If she plans to keep the
term of the loan the same, how much will her monthly repayment reduce?

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