Question

Use the​ future-value formula o to calculate the annual amount that needs to be deposited over a​ 20-year period so that an ordinary annuity accrues​ $100,000 if it earns​ 7.5%, compounded​ annually?

A. $2,209.22

B. ​$2,309.22

C. ​$2,359.22

D. ​$2,300.22

Answer 1

Option (B) is correct

Here, the deposits will be same every year, so it is an annuity. We need to calculate 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 = $100000, P is the periodical amount, r is the rate of interest = 7.5% and n is the time period = 20

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

$100000 = P * ((1 + 7.5%)20 - 1 / 7.5%)

$100000 = P * ((1 + 0.075)20 - 1 / 0.075)

$100000 = P * ((1.075)20 - 1 / 0.075)

$100000 = P * ((4.24785110024 - 1 / 0.075)

$100000 = P * (3.24785110024 / 0.075)

$100000 = P * 43.3046813365

P = $100000 / 43.3046813365

P = $2309.22

So, the amount of money that we need to deposit each year is $2309.22