411.3
3.You're negotiating for a new car. You are going to pay for the
car with a 5-year loan at 7% per year, compounded monthly. Your
loan payments will also be monthly. You've got the price down to
$20,000, but you're still negotiating. For every $100 that you
get the dealer to lower the price of the car, how much does your
monthly payment decrease? Assume your first payment is due one
month from today.
Use the annuity formula to calculate the payment that $100 in PV creates. PV=$100, r=.07/12, n=60, CF=?
\( \large PV = P3 \left [ \frac{1}{r} - \frac{1}{r \left(1+r \right )^{n} } \right ] \)
so
\( \Large $100 = P3 \left [ \frac{1}{\frac{.07}{12}} - \frac{1}{\frac{.07}{12} \left(1+\frac{.07}{12} \right )^{60} } \right ] \).
Solving for P3 we get \( \frac{$100}{50.50199} = $1.98 \)