Question

Your car loan requires payments of $100 per month for the first four years and payments of $400 per month during the fifth year. The annual interest rate is 18% and payments begin in one month. What is the present value of this five-year loan?

Answer 1

Step 1: Present value of first annuity

PMT = 100

n = 4 * 12 = 48 months

r = 18%/12 = 0.015 per month

Step 2: Present value of second annuity

PMT = 400

n = 12

r = 0.015

This gives the present value as of year 4

PV = PV₄/(1 + r)^n

n = 4 * 12 = 48

r = 18%/12 = 0.015

PV = 4,363.0020826667/(1 + 0.015)^48

PV = 4,363.0020826667/2.0434782893

PV = 2,135.0860958553

Step 3: Add the results from step 1 and step 2

The present value of five-year loan = 3,404.2553646667 + 2,135.0860958553

The present value of five-year loan = $5,539.341460522