Question

You are taking out a $25,000 loan for a new car. You will make monthly payments for 5 years. You are given the choice between putting nothing down and a 7% APR OR putting $5000 down and a 5% APR. Which do you choose?

Answer 1

Formula : Installment = P (r/c) (1+ r/c)^nc / (1+ r/c)^nc - 1
Installment (no cash down) = 25000 (0.07/12) (1+ 0.07/12)^(5*12) / (1+ 0.07/12)^(5*12) - 1
Installment (no cash down) = 25000*0.005833333 (1.005833333)^60 / (1.005833333)^60 - 1
Installment (no cash down) = 25000*0.005833333*1.417625 / 1.417625 - 1
Installment (no cash down) = 206.737 / 0.417625 = 495.03
Total payment = 495.03*60= $29701.81
Installment (cash down $5000) = 20000 (0.05/12) (1+ 0.05/12)^(5*12) / (1+ 0.05/12)^(5*12) - 1
Installment (cash down $5000) = 20000*0.004166667*1.2833587/1.2833587 - 1
Installment (cash down $5000) = 106.9466/0.2833587 = 377.42
Total payment = $27645.49
We must opt for Installment on 5% APR with down payment of $5000
because lower installment and lower total payment of $27645.49