Question

How much would you need to deposit in an account each month in order to have $30,000 in the account in 9 years? Assume the account earns 2.5% interest. Round your answer to the nearest cent as needed.

Answer 1

Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $30000. 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 = $30000, P is the periodical amount, r is the rate of interest = 2.5%. Monthly rate = 2.5% / 12 = 0.20833% and n is the time period = 9 * 12 = 108 months

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

$30000 = P * ((1 + 0.208333%)¹⁰⁸ - 1 / 0.20833%)

$30000 = P * ((1 + 0.00208333)¹⁰⁸ - 1 / 0.00208333)

$30000 = P * ((1.0020833333)¹⁰⁸- 1 / 0.002083333)

$30000 = P * (1.25202964433 - 1 ) / 0.002083333)

$30000 = P * (0.25202964433 / 0.002083333)

$30000 = P * 120.9742486342798

P = $30000 / 120.9742486342798

P = $247.99

So, the amount of money that we need to deposit each month is $247.99