Question

You are offered the choice of the following two income streams; - $7,000 every 2 years in perpetuity with the first receipt immediately. $2,000 every quarter for 10 years with the first receipt at the end of the first quarter. The annual interest rate is 6% pa compounded quarterly. Which income stream do you choose? (Answer to the nearest dollar)

please help me to solve the question, and also a cash flow map, thank you!

Answer 1

Annual interest rate in 2 year basis = (1 + Interest Rate / 4)^n = (1 + 6%/4)^8 - 1 = 12.65%

Present Value of Perpetuity = Initial Cash Flow + Cash Flow / 12.65% = 7000 + (7000 / 12.65%) = 62335.97

Present value of option 2 = "PV(rate,nper,pmt)" = "PV(1.50%,40,2000) = $59831.69

i would choose first option of perpetuity as it results in higher present value

HT Quarter Option 1 0 $ 7,000.00 Option 2 $ 2,000.00 $ 2,000.00 $ 2,000.00 $7,000.00 $ 2,000.00 12 13 14 $ 2,000.00 15 16 $ 2,000.00 $ 2,000.00 24 $7,000.00 $71 $ 2,000.00