Question

How much interest is included in the accumulated value of $82.64 paid at the end of each month for four years if interest is 6.5% compounded monthly?

Answer 1

First we will calculate the accumulated or future value. Here, the deposits will be same every month, so it is an annuity. We will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, P is the periodical amount = $82.64, r is the rate of interest = 6.5% compounded monthly, so monthly rate = 6.5% / 12 = 0.54167 and n is the time period = 4 * 12 = 48 months

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

FVA = $82.64 * ((1 + 0.54167%)⁴⁸ - 1 / 0.54167%)

FVA = $82.64 * ((1 + 0.0054167)⁴⁸ - 1 / 0.0054167)

FVA = $82.64 * ((1.0054167)⁴⁸ - 1 / 0.0054167)

FVA = $82.64 * ((1.29602043541- 1 / 0.0054167)

FVA = $82.64 * (0.29602043541/ 0.0054167)

FVA = $82.64 * 54.6495902327

FVA = $4516.27

So, accumulated value is $4516.27

Total amount paid = $82.64 * 48 months = $3966.72

Now,

Interest = Accumulated value - Total amount paid

Interest = $4516.27 - $3966.72

Interest = $549.55