suppose you open up an annuity and make monthly deposits of $250 at 6.99% APR. Y

Question

suppose you open up an annuity and make monthly deposits of $250 at 6.99% APR. You do this for 15 years, but then get a big raise from your employer and so decide to update your deposit to $X so that you can achieve your retirement goal of $900,000 by retirement in 15 more years. 1. What is the balance of your annuity after the first 15 years? 2. If you continued to make the same payment over second 15-year period, how short of your goal would you be? 3. What should X, your new payment, be in order to reach your goal, assuming you deposit $250 per month over the first 15 years and $X per month over the second 15 years?

Explanation / Answer

Note:

If we assume that $ 79171.73 will continue to attract an interest rate of 6.99 % APR for next 15 years, then the maturity value of this deposit will be (79171.73)*[(1.005825)180] =(79171.73)*2. 844701243 = $ 2252199.19. Then the goal gets reduced to $900000-$ 2252199.19 = $ 674780.08 in 15 years so that X = (674780.08)*(0.005825)/ (1.844701243) = $ 2130.75.

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