Question

Suppose you want to buy a car. The dealer offers a financing package consisting of a 3.6% APR compounded month- ly for a term of four years. Suppose that you want your monthly payments to be at most $400. What is the maxi- mum amount that you should finance

Answer 1

Answer:

The answer is "17,856.7431"

Explanation:

Payment (P) $= \frac{iA}{1-(1+i)^{-N}}$

Amount of finance (A)$= \frac{P[1-(1+i)^{-N}]}{i}$

N(number of payments) $= 4 \times 12 = 48$

i= interest rate per month $= \frac{3.6 \%}{12} = \frac{0.036}{12} = 0.003$

$P =\ 400 \\\\A= \frac{400(1-(1+0.003)^{-48}}{0.003}$

   $= \frac{400(1-(1.003)^{-48})}{0.003} \\\\= \frac{400(1- 0.866074427)}{0.003} \\\\= \frac{400(0.133925573)}{0.003} \\\\= \frac{53.5702292}{0.003} \\\\= \ \ 17,856.7431$