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

a) Semi-annual interest = 10,000 x 4% / 2 = 200

For savings account, Effective annual rate, r = (1 + 1%/12)^12 - 1 = 1.005%

Future Value of the savings account can be calculated using FV function

N = 10 x 2 = 20, PMT = 200, I/Y = 1.005%/2, PV = 0

=> Compute FV = $4,196.75

Money after 10 years = $10,000 + $4,196.75 = $14,196.75

b) Effective annual rate can be calculated using TVM equation

Rate = (FV / PV)^(1/n) - 1 = (14,196.75 / 10,000)^(1/10) - 1 = 3.57%