Question

An investor pays $10,000 today to purchase an investment that returns $5,000 at the end of each of years 2, 4, and 5. The returns are immediately reinvested at an annual interest rate of 5%. Calculate the annual effective yield rate for the investor at the end of the fifth year.

(a) 9.91% (b) 12.00% (c) 12.45% (d) 13.11% (e) 15.13%

Answer 1

We first need to calculate the sum of the Future value of the cash inflows at the enf of year 5:

Below is the future value calculation:

Year	CF	Compounding Factor	Compounded CF
2	$        5,000.00	(1+0.05)^(5-2)=	1.157625	1.157625*5000=	$              5,788.13
4	$        5,000.00	(1+0.05)^(5-4)=	1.05	1.05*5000=	$              5,250.00
5	$        5,000.00	(1+0.05)^(5-5)=	1	1*5000=	$              5,000.00
				Future Value = Sum of all Compounded CF	$           16,038.13

Now annual return is calculated as follows:

So the annual return is 9.91% and the correct option is a