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

Initial cost of the investment = $10000

investment returns are,

CF2 = $5000

CF4 = $5000

CF5 = $5000

reinvestment rate r = 5%

So, value of the future cash flow at year 5 using compounding is

Future value at year 5 = CF2*(1+r)^3 + CF4*(1+r) + CF5 = 5000*1.05^3 + 5000*1.05 + 5000 = $16038.13

annual effective yield rate for the investor at the end of the fifth year = (FV/initial cost)^(1/5) - 1

annual effective yield rate for the investor at the end of the fifth year = (16038.12/10000)^(1/5) - 1 = 9.91%

Option A is correct.