Question

Suppose you have decided to put $200 at the beginning of every month in a savings account that credits interest at the annual rate of 6%, but compounds it monthly. Find the amount in this account after 30 years.

Answer 1

Here, the deposits will be same every month, so it is an annuity. We have to find the future value of annuity here. 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 = $200, r is the rate of interest = 6% compounded monthly, so monthly rate = 6% / 12 = 0.5% and n is the time period = 30 * 12 = 360

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

FVA = $200 * ((1 + 0.5%)360 - 1 / 0.5%)

FVA = $200 * ((1 + 0.005)360 - 1 / 0.005)

FVA = $200 * ((1.005)360 - 1 / 0.005)

FVA = $200 * ((6.02257521226 - 1 / 0.005)

FVA = $200 * (5.02257521226 / 0.005)

FVA = $200 * 1004.51504245

FVA = $200903

So, the amount in the account after 30 years will be $200903.