Suppose you invest $140 at the end of each month for 5 years into an account earning 9% annual interest compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 22 years. How much will you have in the end?

Respuesta :

Answer:

 $75,915.92

Step-by-step explanation:

You want the value of an annuity of $140 per month for 5 years at 9% compounded monthly, after it has accumulated interest for 22 more years.

Annuity

The formula for the future value of an ordinary annuity is ...

  A = P(n/r)((1 +r/n)^(nt) -1)

where P is the periodic payment made n times per year for t years and the account earns annual interest rate r.

The value of $140 monthly payments after 5 years is ...

  A = $140·(12/0.09)((1 +0.09/12)^(12·5) -1) = $140(1.0075^60 -1)/0.0075

  A ≈ $10559.38

Compound interest

That annuity balance will then earn interest compounded monthly for another 22 years. Its value will become ...

  A = ($10559.38)(1.0075^(22·12)) ≈ $75,915.92

You will have about $75,915.92 in the end.

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Additional comment

An actual account would have the interest amount rounded monthly, so the final value would be slightly different from the values calculated here. Usually the difference is on the order of a dollar or so.

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