Question

Your car loan requires payments of 200 per month for the first year and payments of 400 per month during the secound year the annual interest rate is 12% and payment beings in one month. what is the present value of this two-year loan?

Answer 1

As the payments are made monthly, so first we need to convert it into the monthly interest rate.

(1 + EAR) = (1 + r)¹²

r = (1.12)^1/12 - 1

r = 0.9489% (This is rate per period.)

This loan consists of two annuities: $200 per month and $400 per month.

First finding the PV of the $200 annuity.

P is periodic payment = 200,

n is number of periods = 12

PV = $2,258.29

Now, for the second annuity, we first need to find its PV at the end of year 1 and then discount it back for 1 year to find the PV today.

PV at the end of year 1.

PV = $4,516.57

Now, discount it back for 1 year @ an annual interest rate of 12% to find the PV today.

PV = $4,516.57/(1.12) = $4032.65

Now, add the PV of both the annuities.

PV of loan = 2258.29 + 4032.65 = $6290.94