Question

Troy is saving for his retirement 22 years from now by setting up a savings plan. He has set up a savings plan wherein he will deposit $ 127.00 at the end of each month for the next 11 years. Interest is 7 % compounded monthly.

(a) How much money will be in his account on the date of his​ retirement? ​

(b) How much will Troy ​contribute?

​(c) How much will be​ interest? ​

(a) The future value will be ​$ . ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.) ​

(b) Troy will contribute ​$ ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.) ​

(c) The interest will be ​$ ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

Effective monthly rate = 7%/12 = 0.5833333333%

n = 22 years * 12 = 264

a)

$FV = \frac{ CF_{1}}{r} * \left [ (1+r)^{n} - 1 \right ]$

$FV = \frac{127}{0.005833333333} * \left [ (1+0.005833333333)^{264} - 1 \right ]$

b) Troy will contribute 127*264 = $33,528

c) Interest will be 79,329.9962349259 - 33,528 = $45,801.9962349259

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