Question

A car loan requires 60 monthly payments of $250 and has a 6% APR.1 (a) What is the present value of the loan one month before the first payment is due? 

Answer 1

Interest rate per annum = 6% (6%/12 = 0.005 per month)

Total payments: $250.25

Payment (PMT) = $250 per month

n = 60 monthly payments

Future value (FV)

$FV = PMT * \frac{(1-(1+r)^{-n}}{r}$

$FV = 250 * \frac{1-(1+0.06)^{-60}}{6\%/12}$

$FV = 250 * \frac{1-(1.06)^{-60}}{0.005}$

$FV = 250 * \frac{(1-0.030314)}{0.005}$

$FV=250 * \frac{0.969686}{0.005}$

FV = 48,484.30

Present value of the loan one month before the first payment is due

PV = FV / (1+r) ⁿ

PV = $48,484.30 / (1+0.005)^{60}$

PV = $48,484.30 / (1.005)^{60}$

PV = 48,484.30 / 1.34885

PV = $ 35,944.92