SOLUTION: Suppose you invest $200 a month for 4 years into an account earning 8% compounded monthly. After 4 years, you leave the money, without making additional deposits, in the account fo

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Question 1203142: Suppose you invest $200 a month for 4 years into an account earning 8% compounded monthly. After 4 years, you leave the money, without making additional deposits, in the account for another 21 years. How much will you have in the end?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

First we compute the future value of depositing periodic payments of $200 a month for 4*12 = 48 months.
FV+=+P%2A%28%281%2Bi%29%5En+-+1%29%2Fi

FV+=+200%2A%28%281%2B0.08%2F12%29%5E48+-+1%29%2F%280.08%2F12%29 (note that i = 0.08/12)

FV+=+11269.9830130137

FV+=+11269.98

The account is valued at $11,269.98 after the four years are up.

That money is then treated as a deposit into an account with the same interest rate and compounding frequency.
The money is not touched for 21 years (aka 21*12 = 252 months)

Use the compound interest formula
A+=+P%2A%281%2Br%2Fn%29%5E%28n%2At%29

A+=+11269.98%2A%281%2B0.08%2F12%29%5E%2812%2A21%29

A+=+60133.5137078229

A+=+60133.51

Answer: $60,133.51