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You deposit $400 each month into an account earning 7% interest compounded monthly. a) How much will you have in the account in 15 years?

User Dinh Quan
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It is a classic Ordinary Annuity saving plan. The general formula is

FV = P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29, (1)

where FV is the future value of the account; P is the monthly payment (deposit); r is the monthly percentage yield

presented as a decimal; n is the number of deposits (= the number of years multiplied by 12, in this case).

Under the given conditions, P = 400; r = 0.07/12; n = 12*20 = 240. So, according to the formula (1), you get

at the end of the 20-th year

FV = 400%2A%28%28%281%2B0.07%2F12%29%5E%2812%2A20%29-1%29%2F%28%280.07%2F12%29%29%29 = 400%2A%28%28%281%2B0.07%2F12%29%5E240-1%29%2F%28%280.07%2F12%29%29%29 = $208,370.70.

Note that you deposit only 12*20*$400 = $96,000.

The rest $208370.70 - $96000 = $1212370.70 is the interest what the account earns/accumulates in 20 years.

User Xxg
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