Chapter 3, Section 2
1.
Calculate the present value of an annuity that pays 100 at the end of each year for
20 years.
The annual effective interest rate is 4%.
2.
Calculate the present value of an annuity that pays 100 at the end of each month
for 20 years.
The nominal interest rate is 12% compounded monthly.
3.
Calculate the present value of an annuity that pays 100 at the end of each month
for 20 years.
The annual effective interest rate is 12%.
4.
Erin invests 1000 at the end of each year for 10 years.
She earns an annual
effective interest rate of 6%.
How much will she have at the end of 10 years?
5.
Mike wants to buy a car in five years.
He wants to have saved 50,000 to buy the
car at that time.
If Mike earns 8% compounded monthly, how much must he
invest at the end of each month for the next five years?
6.
James buys a car today by taking a loan of 50,000.
This five year loan has an
nominal interest rate of 8% compounded monthly.
Calculate the monthly loan
payments that James must make at the end of each month for the next five years.
7.
Heather won the lottery!
She has the following payout options:
a.
One million at the end of each year for the next 20 years; or
b.
A lump sum of 7,469,443.62.
Calculate the annual effective interest rate at which both options have the same
present value.
8.
Josephine is paying a car loan with payments of 200 at the end of each month.
The loan has a monthly effective interest rate of 1%.
If the car loan is for
7,218.90, calculate the number of payments that Josephine will need to make.
9.
For a given interest rate,
= 14.2068 and
= 8.3064.
Calculate n.
10.
If d = 0.05, calculate
.
11.
The accumulated value of an n year annuity is four times the present value of the
same annuity.
Calculate the accumulated value of 100 in 2n years.
(Note:
This is
NOT asking for the accumulated value of an annuity
–
just the accumulated value
of a single payment of 100.)
12.
No. 2 in the book.
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Chapter 3, Section 3
13.
John’s father is paying him 500 at the beginning of each month for the next four
years while he is in college.
Calculate the present value of this annuity on the
date of the first payment using an interest rate of 9% compounded monthly.
14.
Sarah is depositing 300 into an account at the start of each quarter.
How much
will she have at the end of 4 years at an interest rate of 7% compounded
quarterly?
15.
At the start of each month for 50 months, Julia deposits 100 into her bank
account.
At the end of 50 months, Julia has 6084.72.
Calculate the annual
effective interest rate being earned by Julia.
16.
Kathy wants to accumulate a sum of money at the end of 10 years to buy a house.
In order to accomplish this goal, she can deposit 80 per month at the beginning of
the month for the next ten years or 81 per month at the end of the month for the
next ten years.
Calculate the annual effective rate of interest earned by Kathy.
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 Fall '08
 Staff
 Math, Time Value Of Money, Interest, Nominal Interest Rate, Mortgage loan

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