Question

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.

How much will the face value of the bond that you will be investing?

Please calculate the monthly payment in your retirement account in order to be able to achieve the plan mentioned above?

How much will your inheritors receive?

Answer 1

Given that the annual Expenses after retirement are $50,000

Accordingly, Investment value should be 50000/0.06 = 833333

Total Number of years upto retirement is 30

Hence we have to make annuity for a period of 30years.

We know future value of annuity is

Future Value of Annuity = A * ((1+r)ⁿ - 1)/r

833333 = A * ((1+0.07)³⁰ -1)/0.07

A = 8822 per Annum

Hence the investment Amount should be $8822 per annum

Calculation of monthy payment

When Annual Interest is 7% we will find out monthly interest as follows

Let Monthly interest is X now (1+X)¹² = 1.07( Monthly interest compounded will make 7% per year)

Now X = 0.5654% Approx.

Again we can use the formula for Future Value of annuity as shown above

833333 = A * ((1+0.005654)^12*30-1)/0.005654

Hence A = 619$ Per month

Please note that we will invest an amount of 833333 in bonds inorder to get monthly $50,000 annual copoun. We will be getting that copoun till the end and our inheritors will get the bond face value amount i.e $8,33,333.