Question

Suppose you will invest $1,500 each year at the interest rate of 9.3%, beginning one year from now. Assuming the interest rate compounds annually, what will be the total future value of these investments 30 years from now?

Answer 1

Here, the deposits will be same every year, so it is an annuity. We need to calculate the future value of annuity. We will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $1500, r is the rate of interest = 9.3% and n is the time period = 30

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

FVA = $1500 * ((1 + 9.3%)30 - 1 / 9.3%)

FVA = $1500 * ((1 + 0.093)30 - 1 / 0.093)

FVA = $1500 * ((1.093)30 - 1 / 0.093)

FVA = $1500 * ((14.40803844 - 1 / 0.093)

FVA = $1500 * (13.40803844 / 0.093)

FVA = $1500 * 144.172456344

FVA = $216258.68

So, future value of investments will be $216258.68.