Question

Mark wants to save money for a down payment on a house that he wants to buy in 5 years. He starts with $2000 in an investment account and adds $125 each month. He chooses an investment type that compounds once a month and averages 5% interest. How much money will he have in 5 years?

please help :(

Answer 1

$11,067.48

Explanation:

You want to know the value in 5 years of a $2000 investment at 5% interest compounded monthly, to which $125 is added each month.

Future value

The value of the $2000 investment is given by the compound interest formula:

A = P(1 +r/n)^(nt)

A = 2000(1 +0.05/12)^(12·5) ≈ $2566.717

Annuity

The value of an ordinary annuity of $125 per month for 5 years at 5% interest is ...

A = 125((1 +0.05/12)^(12·5) -1)/(0.05/12) ≈ 8500.760

Total

The sum of these values is ...

investment value = $2566.72 +8500.76 = $11,067.48

Mark will have $11,067.48 in 5 years.

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Additional comment

This problem is solved here by breaking it into parts for which we have formulas. The attached calculator solution gives the combined effect of a non-zero present value and a series of payments.

The payments are presumed to be made at the end of the month, so the final payment earns no interest before it is withdrawn. (This is why it is called an ordinary annuity.)

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