Question

Red Company invested $20,000 in a fund that was earning interest at a rate of 4.00% compounded semi-annually. After 3 years and 6 months, the company transferred these funds to another investment that was earning interest at 4.50% compounded monthly.

a. What is the balance in the fund at the end of 3 years and 6 months?

Round to the nearest cent

b. What is the balance in the fund at the end of 6 years (from the initial investment)?

Round to the nearest cent

c. By what amount did the fund grow during the 6 year period?

Round to the nearest cent

Answer 1

(a) Balance in the fund at the end of 3 years and 6 months: Period (3 years&6months) = 7 semi annual years Present value = $20,000 Interest rate per semi annual = 4.00% Future Value = Present value *(1+r)^n = $20,000 *(1+0.04)*7 = $20,000 * 1.3159 = $26,318 (b) Balance in the fund at the end of 6 years (from initial investment): Additional period = 12 semi annual years - 7 semi annual years = 5 semi annual years Present value = $26,318.00 Interest rate per semi annual = 4.50% Future Value = Present value *(1+r)^n = $26,318 *(1+0.045)45 = $26,318 * 1.2462 = $32,797.49 © Amount grow from initial amount to after 6 years period: = amount balance after 6 years - Initial amount = $32,797.49 - $20,000 = $12,797.49