Question

Jill invests a sum of money in a savings account with a fixed annual interest rate of 7.30% compounded 4 times per year. After 6 years, the balance reaches $8,487.70. What was the amount of the initial investment?

Answer 1

$5499

Explanation:

The interest of $100 for 1 year is $7.30.

So, the interest for $100 for 4 months is 7.30/4 =$1.825.

Now, there are (6×4) =24 quarters in 6 years.

If the sum of money invested is $x, then it will grow up to $8487.70 at a rate of 1.825% interest quarterly after 6 years.

Therefore, we can write
`x[1+(1.825)/(100)] ^(24)= 8487.70`

⇒ x[1.5435] =8487.70

⇒ x = 5499

Therefore, the amount of initial investment is $5499. (Answer)