Consider the annual cash flows shown in the diagram below If

Consider the annual cash flows shown in the diagram below:

If the interest rate for the first four years is 7% APR compounded monthly and the interest rate for the last 2 years is 10% APR compounded quarterly, what is the equivalent amount P?

Solution

We first compute the equivalent annual rate, EAR.

EAR for 7% APR compounded monthly = [1 + (0.07/12)]¹² - 1 = [1 + 0.0058]¹² - 1 = 1.0719 - 1 = 7.19%

EAR for 10% APR compounded quarterly = [1 + (0.10/4)]⁴ - 1 = [1 + 0.025]⁴ - 1 = 1.1038 - 1 = 10.38%

P ($) = [200 / (1.0719)] + [400 / (1.0719)²] + [600 / (1.0719)³] + [800 / (1.0719)⁴] + [500 / (1.1038)⁵] + [500 / (1.1038)⁶]

= 186.58 + 348.14 + 487.18 + 606.00 + 305.15 + 276.46

= 2,209.51