Question

You are considering two different strategies for a savings account that you intend to close exactly 30 years from today. For Strategy 1, deposit $200 per month for 5 years (first deposit today; last one exactly 5 years from today); no new deposits will be made after the end of the deposit period, but interest continues to accrue until the account is closed. For Strategy 2, you’ll make your first monthly deposit exactly 5 years from today, each monthly deposit also equals $190, and you’ll continue making monthly deposits for 25 years, so that you make the final deposit exactly 30 years from today when you close the account. The savings rate always is 6.00% compounded monthly.

Find the difference in the Present Values of the two strategies.

Answer 1

It is given in the question that last payment is made in exactly 5 years from today and first payment is today. This means there is an additional payment at the end of 5th year.

In strategy 1, there are total 61 payments (including last payment).

The present value for strategy 1 is calculated below:

Present value = 200 x 1 - 1.005-61 11 - 1.005-1

Present value = 200 X 52.72556075

Present value = 10,545.11215

In strategy 2, there are total 301 payments.

Present value = 190 x 1 - 1.005 -301 (1-1.005-1) X 1.005-60

Present value = 200 x 22,003.41091

Present value = 22,003.41091

The difference between present values is $22,003.41091 - $10,545.11215 = $11,458.29876.