Please answer each of the following questions in detail and provide in-text citations in support
of your argument. Include examples whenever applicable. Make sure to provide examples for
each of the questions below.
a. Discuss how time value of money in the context of compounding interest.
b. Explain what an annuity is and what are the two most common types of annuity. Explain
how the present value and future value of an annuity is determined.
c. Extend the notion of compounding mentioned in your answer to part a above to
general situations where compounding is induced by growth, inflation, or deflation.
By the end of this year you would be 35 years old and you want to plan for your retirement.
You wish to retire at the age of 65 and you expect to live 20 years after retirement. Upon
retirement you wish to have an annual sum of $50,000 to supplement your social security
benefits. Therefore, you opened now your retirement account with 7% annual interest rate. At
retirement you liquidate your account and use the funds to buy an investment grade bond
which makes $50,000 annual coupon payments based on a 6 % coupon rate, throughout your
1. How much will the face value of the bond that you will be investing?
2. Please calculate the monthly payment in your retirement account in order to be able to
achieve the plan mentioned above?
3. How much will your inheritors receive?
Now lets extend the problem so that you protect yourself against inflation.
Suppose you think if you were to retire right now you would have needed $50,000 each year to
supplement your social security and maintain your desired lifestyle. But because there is on
average 3% annual inflation, when you retire in 30 years from now you need more than
$50,000 per year to maintain the lifestyle you like.
4. How much will be equivalent to $50,000 at the retirement time when adjusted for
5. How much will be the face value of the bond that yields the equivalent of $50,000, found
in #4 of Part B in coupon payment?
6. How much annual payment in the retirement account is needed to accumulate the
amount needed to purchase the bond when retiring?
7. What is the purchase power of the amount that will be received by your inheritors,
measured in the current value of $ at the time of opening the retirement account?
(Hint: First calculate what future amount in 30 years, which is equivalent to $50,000 of now and
then solve the rest of the problem).