Question

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.

How much will be equivalent to $50,000 at the retirement time when adjusted for inflation?

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?

How much annual payment in the retirement account is needed to accumulate the amount needed to purchase the bond when retiring?

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).

Hello the first question is the following one;

Part A:

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 retirement years.

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 let’s extend the problem so that you protect yourself against inflation.

Answer 1

Given, inflation= 3% per year

Amount at the time of retirement (in 30 years) equivalent to $50,000 now= 50,000*(1+3%)^30

= $121,363.12

Face value of bond= C/r

Where

C= annual coupon ($121,363.12 as above) and r= coupon rate (given in part A as 6%)

Plugging the values,

Face value of the bond= $121,363.12 / 0.06 = $ 2,022,718.73

Given,

Interest rate on retirement account= 7%

Annual payment needed to accumulate $ 2,022,718.73 in the retirement account= $21,413.32

Calculation as follows:

Inheritors will receive face value of the bond.

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= F/(1+i%)^n

Where F= Face value of bond ($ 2,022,718.73 as above), i= inflation rate (3%) and n= period till retirement (30 years)

Plugging the values,

Purchasing power at the time of opening retirement account= 2,022,718.73/(1+3%)^30

= $ 833,333.33