Question

Compute the present value of $3,000 paid in four years using the following discount rates: 3 percent in year 1, 4 percent in year 2, 5 percent in year 3, and 6 percent in year 4

Answer 1

Present value=Cash flow in year 1/(1+discount rate in year 1)^1+Cash flow in year 2/(1+discount rate in year 2)^2+Cash flow in year 3/(1+discount rate in year 3)^3+Cash flow in year 4/(1+discount rate in year 4)^4
Given that discount rate in year 1=3%
Discount rate in year 2=4%
Discount rate in year 3=5%
Discount rate in year 4=6%
Cash flow for each year=$3000

Present value=3000/(1+3%)^1+3000/(1+4%)^2+3000/(1+5%)^3+3000/(1+6%)^4
=3000/(1.03)^1+3000/(1.04)^2+3000/(1.05)^3+3000/(1.06)^4
=3000/1.03+3000/1.0816+3000/1.157625+3000/1.26247696
=2912.621359+2773.668639+2591.512796+2376.28099
=$10654.08378