Question

Barry wishes to save $10,000 for a holiday in 2 years’ time. Twenty-four equal monthly deposits will be made into an account, the first deposit being made immediately. The account earns interest at 7%p.a compounding monthly. What is the size of his monthly deposit?

Select one:

a. $387.13

b. $358.96

c. $320.12

d. $333.21

Answer 1

Option (a) is correct

Here, the deposits will be same every month, so it is an annuity. And since the deposits will start at the beginning of each month so it will be termed as an annuity due. For calculating the monthly deposits, we will use the folowing future value of annuity due formula:

FVAD = (1 + r) * P * ((1 + r)n  - 1 / r)

where, FVAD is future value of annuity due = $10000, P is the periodical amount, r is the rate of interest = 7% compounded monthly, so monthly rate = 7% / 12 = 0.58333% and n is the time period = 2 * 12 = 24 months

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

$10000 = (1 + 0.5833%) * P * ((1 + 0.58333%)24 - 1 / 0.5833%)

$10000 = (1 + 0.0058333) * P * ((1 + 0.0058333)24 - 1 / 0.0058333)

$10000 = (1.0058333) * P * ((1.0058333)24 - 1 / 0.0058333)

$10000 = (1.005833) * P * ((1.14980592605 - 1) / 0.0058333)

$10000 = (1.00583333) * P * (0.14980592605 / 0.0058333)

$10000 = (1.0058333) * P * 25.6808894736

$10000 = 2.58308232111 * P

P = $10000 / 25.8306938061

P = $387.13

So, monthly payments are $387.13