Question

Find how many years it would take for an investment of $2300 to grow to $7100 at an annual interest rate of 7.7% compounded quarterly.

Answer 1

15 years

Explanation:

7100 = 2300 × (1 + 7.7/400)^n

1.01925^n = 71/23

n ln(1.01925) = ln(71/23)

n = 59.11690111 quarters ÷ 4

= 14.77922528

Answer 2

The formula to calculate the amount of money in this case:

A = Principal x (1 + rate/4)^(year x 4)

=> 7100 = 2300 x (1 + (7.7/100)/4)^(year x 4)

=> 1.026^(year x 4) = 7100/2300

=> 1.019^(year x 4) = 3.087

=> year x 4 = log(3.087)/log(1.019)

=> year x 4 = 59.89

=> year = 59.89/4

=> year = 14.97 = ~15

Hope this helps!

:)