Lukas Roth
FIN 305W
Practice Problems: Annuities and Perpetuities
Problem #1
In 21 years you want to receive $25,000 income annually to perpetuity.
What equal
annual deposits are required to guarantee that income if you start in one year and make
your last payment in 20 years. The interest rate is 10%.
Problem #2
You have been offered the life insurance policy “Oh, what a deal.” As part of that policy,
you invest $100,000 today and are promised $500,000 in 20 years.
Carefully answer the
following questions.
A.
What average annual rate of return is the policy promising?
Assume annual
compounding.
B.
Suppose the insurance company can invest your money at 10%.
What equal annual
fee can it pay itself from the difference between 10% and the rate it is implicitly
promising?
Problem #3
Suppose the Township of State College wants to subsidize firms that agree to locate here.
It is thinking of various alternatives.
Assume the annual market rate of interest is 8%.
Carefully answer the following questions.
A.
To induce firms to commit to the local economy, it could give them three equal
lump
sums
of $100,000 every year starting in three years.
What would be the current value
of the associated subsidy?
B.
It could give them a five-year, interest-free $2,000,000
loan
.
What would be the
current value of this subsidy?
C.
It could give them a
lump-sum perpetuity
of $20,000 starting at the end of year five.
What would be the current value of this subsidy?
Problem #4
You just turned 40 and will retire at the end of 65.
It is therefore time to start planning
for your retirement.
Based on statistical information you expect to live until the end of
85.
You are asking yourself a number of questions, listed in what follows.
Carefully
answer them by assuming a annual interest rate of 4% (annual compounding).
A.
Suppose you need an annual income of $100,000 to maintain your life standard.
How
much money do you have to set aside every year to be able to pay yourself $100,000
per year when you retire?
Assume your first contribution is in one year, and the last
one at the end of your 65th year (i.e., at the beginning of year 66).
Moreover, assume
you receive your first payment at the end of year 66 (one year after the last
contribution), and the last one at the end of year 85.

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