Question

An annuity pays $5000 each year for 5 years starting today. It pays $6000 per year for year 7 to year 10. The interest rate are 4% for the first 5 years and 8% for years 6 to 10. What is the present value of these cash flows?

Answer 1

Solution:

Calculation of Present value of ordinary annuity

First cash flow is received today,hence it is not require to be discounted:

Present value=Cash flows/(1+interest rate)^no. of years

=$5000+$5000/(1+0.04)^1+$5000/(1+0.04)^2+$5000/(1+0.04)^3+$5000/(1+0.04)^4+$6000/(1+0.08)^6+$6000/(1+0.08)^7+$6000/(1+0.08)^8+$6000/(1+0.08)^9

=$23,149.48+$13525.07

=$36,674.55