Question

13. $15,000 is invested in an account that yeilds 5% interest per year. After how many years will the account be worth $91,221.04 if the interest is compounded yearly?

Answer 1

The correct answer is 37 years.

Explanation:

Principal (P) invested is $15000

Rate of interest (r) per year is 5% compounded yearly.

Amount (A) of the principal is $91221.04.

Let the principal is invested for x years (t).

According to the problem,

A = P +
`(1 + (r)/(100) ) ^(t)`

⇒ 91221.04 = 15000 ×
`(1 + (5)/(100) ) ^(x)`

⇒ 6.08140267 =
`(1 + (5)/(100) ) ^(x)`

⇒ x = 37

Thus the principal is supposed to be invested for 37 years for it to yield that amount.