You have decided that you will need $350,000 above what your current retirement

Question

You have decided that you will need $350,000 above what your current retirement plan contains to survive and have a little fun when you retire. At the age of 30, you decide to start putting an amount into an annuity once a month. The account earns 5.5% compounded monthly. You plan to retire at the age of 65. Your savings plan is for exactly 35 years.

1. How much will you need to put into this plan each month?   

2. How much total will you put into this plan?

3. How much interest did this plan earn while investing during the 35 years?

4. Before you retire, you decide that you will not take all of the money out at once. Instead, you would like to draw equal monthly payments out until you are 80. Assume the interest stays the same. How much can you draw out each month over this 15-year period?

5. How much did the annuity pay you in interest over this 15-year period?

The purpose of this project is to broaden your awareness of how saving just a small amount per month over the years working in a career combined with the interest your investment will earn becomes a substantial savings for your retirement. In recapping what you have just calculated, please answer the following questions.

Remind yourself of how little you contributed per month_______________________

Remind yourself of how much you actually invested in the plan_______________

6. What was the total dollars the plan paid you in retirement?

7. How much of this was earned from interest (remember this amount will include the interest earned while investing in the plan and while receiving money from the plan)?

So basically the amount you contributed to your retirement was approximately what percentage of the total amount received?

8. 10% , 25%, 50%, 75%

Explanation / Answer

Value of the investment should be $350,000 at the time of retirement, so FV = 350000

Since we are not bothered about the present investment amount in the account, we take PV of this investment as 0

Interest rate would be 5.5%/12, since it is compounded monthly

no of installments = 35*12

1) Amount needed to put in each month can be calculated as follows

=PMT(5.5%/12,35*12,0,-350000,0) = $275.39

Here last 0 is to represent that investment is made at the end of the month

2) Total amount put into this investment $275.39 for 35 years each month

= 275.39 * 35 * 12 = $115,663.93

3) Total interest earned by this investment = Future value - Total investment made

= 350,000 - 115,663.93 = $234,336.07

4) Now we have to find out what will this investment pay monthly for 15 years

This can be calculated as follows

=PMT(5.5%/12,15*12,350000,0,0) = $2,859.79

Here interest rate would be same,

No. of payments would be 15*12 = 180

350000 would be present value, 0 is the future value and last 0 representa investment pays at the end of the month

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