Question

Given a rate of return of 6.85% compounded annually, how much must be deposited at the end of each year for the next 18 years, to accumulate $250,000.

Answer 1

Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $250000. 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 = $250000, P is the periodical amount, r is the rate of interest = 6.85% and n is the time period = 18

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

$250000 = P * ((1 + 6.85%)¹⁸ - 1 / 6.85%)

$250000 = P * ((1 + 0.0685)¹⁸ - 1 / 0.0685)

$250000 = P * ((1.0685)¹⁸ - 1 / 0.0685)

$250000 = P * ((3.29565298882- 1 / 0.0685)

$250000 = P * (2.29565298882/ 0.0685)

$250000 = P * 33.5131823186

P = $250000 / 33.5131823186

P = $7459.75

So, the amount of money that we need to deposit each year is $7459.75