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Starting at age​ 50, a woman puts ​$1600 at the end of each quarter into a retirement account that pays​ 7% interest compounded quarterly. When she reaches age​ 60, she withdraws the entire amount and places it in a mutual fund account that pays​ 9% compounded monthly. From then on she deposits ​$400 in the same mutual fund at the end of each month. How much is in the account when she reaches age​ 65?

Respuesta :

Answer:

$179,187.

Explanation:

Firstly, we need to calculate the future value of her retirement account 10 year form now (at age 60):

Future value of retirement account at age 60 = 1,600 x [1 + (7%/4)] + 1,600 x [1 + (7%/4)]^2 + ... + 1,600 x [1 + (7%/4)]^40 = 94,777.

Secondly, we need to calculate the future value of mutual fund account (funds withdrawn from retirement account).

Future value of mutual fund account (1) at age 65 = 94,777 x [1 + (9%/12)]^60 = 148,391.

Finally, we need to calculate the future value of mutual fund account (funds from her deposit).

Future value of mutual fund account (2) at age 65 = 400 x [1 + (9%/12)] + 400 x [1 + (9%/12)]^2 + ... + 400 x [1 + (9%/12)]^60 = 30,796.

So, when she reach age 65, she will have 148,391 + 30,796 = 179,187.

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