Question

1. Calculate the present value of an annuity stream that pays $20,000 every year for 5 years on the last day of each year if your investment pays 20% compounded quarterly?
2. Calculate the future value of $20,000 invested today for 6 years if your investment pays 4% compounded annually
3. Calculate the future value of an annuity stream that pays $6,000 every year for 5 years on the last day of each year if your investment pays 10% compounded semi annually?

Answer 1

1.

Annual interest rate, Compounded quarterly = 20%

Quarterly interest rate = 20%/4 = 5% = 0.05

Effective annual interest rate = 1.05⁴ – 1 = 0.2155 = 21.55%

Present value of annuity = Annuity amount * {1-(1+r)^-n}/r

Present value of annuity stream = $20,000*(1-1.2155^-5)/0.2155 = $57,827.61

2.

Future value of investment = Amount invested*(1+r)ⁿ

Future value = $20,000*1.04⁶ = $25,306.38

3.

Annual interest rate, compounded semi-annually = 10%

Semi-annual interest rate = 10%/2 = 5% = 0.05

Effective annual interest rate = 1.05² – 1 = 0.1025 = 10.25%

Future value of annuity = Annuity amount*{(1+r)ⁿ-1}/r

Future value of annuity stream = $6,000*(1.1025⁶-1)/0.1025 = $46,586.71