Question

How much interest will you have earned if you save $250 per month for 25 years at 9% interest compounded monthly?

Answer 1

Here, the deposits will be same every month, so it is an annuity. First we will calculate the future value of the payments. We will use the following future value of annuity formula:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, P is the periodical amount,= $250, r is the rate of interest = 9% compounded monthly. So, monthly rate = 9% / 12 = 0.75% and n is the time period = 25 * 12 = 300 months

Now, putting these values in the above formula, we get,

FVA = $250 * ((1 + 0.75%)³⁰⁰ - 1 / 0.75%)

FVA = $250 * ((1 + 0.0075)³⁰⁰ - 1 / 0.0075)

FVA = $250 * ((1.0075)³⁰⁰ - 1) / 0.0075)

FVA = $250 * ((9.40841452988 - 1) / 0.0075)

FVA = $250 * (8.40841452988 / 0.0075)

FVA = $250 * 1121.12193732

FVA = $280280.48

So, future value of the payments = $280280.48

Total payments made = $250 * 300 = $75000

Total interest earned = Future value - Total payments

Total interest earned = $280280.48 - $75000

Total interest earned = $205280.48