Question

A graduating high school student decides to take a year off and work to save money for college. The student plans to invest all money earned in a savings account earning 6% interest, compounded quarterly. The student hopes to have $6000 by the time school starts in 12 months. How much money will the student have to save each month?

Answer 1

Answer:

$488.89

Explanation:

Data provided in the question:

Interest rate = 6% = 0.06

Since the interest is compounded quarterly, n = 4

Interest rate per period = 0.06 ÷ 4 = 0.015

Time = 12 months i.e 1 year

Future value = $6,000

Therefore,

Annuity per quarter = Future value × $[\frac{r}{(1+r)^n-1}]$

or

Annuity per quarter = $6,000 × $[\frac{0.015}{(1+0.015)^4-1}]$

or

Annuity per quarter = $6,000 × 0.244

or

Annuity per quarter = $1466.67

Therefore,

Deposits per quarter = Annuity per quarter ÷ Number of months per quarter

= $1466.67 ÷ 3

= $488.89