Question

You plan on retiring in 20 years. You plan on making an annual payment to yourself in retirement and the first payment will occur 20 years from today. You plan on needing to make 25 payments as you plan to live 25 years in retirement. To keep up with inflation, you want your retirement payments to grow 3% ann. As part of your retirement planning, you deposited $75,000 into a savings account 8 years ago.

However, life etc. got in the way and you have not saved any money since then. After taking this course you realize you need to restart saving if you ever hope to retire and thus starting exactly 6 years from today you plan on becoming disciplined and making semi-annual payments into a savings account. You believe that you will be able to make 15 semi-annual payments of $4,000, (all payments will be of equal size), and then your lifestyle will be such that all investing for retirement will stop. If the discount rate is 7% ann., how much will you be able to take out of your retirement account on your first day of retirement and still be able to satisfy the rest of your retirement criteria?

Answer 1

Amount available at the time of retirement is the sum of the following:

(i)   Future value of $75,000 deposited 8 years ago. Total tenure is 8 + 20= 28 years.

Future value= A*(1+r)^n

Where A= present value (given as $75,000), r= interest rate (given as 7%) and n= period (28 years)

Substituting the values, Future Value= 75000*(1+7%)^28 = $498,662.88

(ii)   Future value of annuity due of 15 semiannual payments of $4000, as on the date of retirement.

The annuity will commence immediately after 6 years. Since the number of payments is 15, retirement (in 20 years from now) will be after 6.5 years from the completion of annuity.

FV of annuity on retirement= $99,901.66 as follows:

Total amount available on retirement= $498,662.88 + $99,901.66 = $598,564.54

Retirement payments constitute a growing annuity due for 25 years, with growth rate of 3%.

First payment of the annuity due= $38,980.27 as follows: