Question

3) Ravi invests $10,000 in an investment account that pays 4% compounded semi-annually. Ravi takes each interest payment and invests it in a savings account that pays 1% compounded monthly.

a) How much money does Ravi have at the end of 10 years?

b) What is the effective annual rate he earned over 10 years?

Answer 1

(3) Initial Investment = $ 10000, Interest Rate = 4% compounded semi-annually, Interest Account Investment Rate = 1 % compounded monthly, Total Tenure = 10 years or (2 x 10) = 20 semi-annual periods

The investor lets the interest accrue for a 6-month period, then takes that interest earned and invests the same in a savings account paying 1% compounded monthly. Now when the interests are taken away after every 6-months, the investment value for each period remains fixed at $ 10000

Effective 6-Month Rate of Savings Account = [1+(0.01/12)]^(6) - 1 = 0.005 or 0.5 %

Interest Accrued every 6-Months = 10000 x 0.04 x 0.5 = $ 200

The first interest is received at the end of the first Semi-annual period and is subsequently accrued for the next 19 semi-annual periods.

Total Future Value of Semi-Annual Interests = 200 x (1.005)^(19) +...............+ 200 = 200 x [{(1.005)^(20)-1}/{(1.005)-1}] = $ 4195.82

Total Account Value at the end of 10 Years = 4195.82 + 10000 = $ 14195.82

Let the effective annual rate be R

Therefore, 10000 x (1+R)^(10) = 14195.82

R = [(14195.82/10000)^(1/10)-1] = 0.03566 or 3.566 % ~ 3.57 %