Understanding Car Payments

Mark wants a go-cart. Mark wants a go-cart. A go-cart costs $500. A go-cart costs $500. Mark only has $100. This is his Down Payment. Mark only has $100. This is his Down Payment. Mark borrows $400 from the bank. Mark borrows $400 from the bank.

The bank doesn’t lend money for free. The bank doesn’t lend money for free. The bank charges Mark 7% on whatever he hasn’t paid off each month. The bank charges Mark 7% on whatever he hasn’t paid off each month. Mark wants to pay off the $400 in 12 months. Mark wants to pay off the $400 in 12 months.

Mark wants to make the same payment each month. Mark wants to make the same payment each month. How much is Mark’s go-cart payment? How much is Mark’s go-cart payment? Answer: $34.61 Answer: $34.61

12 months 12 months 7% interest rate 7% interest rate.07 / 12 =  This is the monthly interest rate.07 / 12 =  This is the monthly interest rate * 400 = $ * 400 = $2.33

The First Month Mark pays $34.61 each month Mark pays $34.61 each month $34.61 $2.33 Goes toward Interest Goes toward the $400 he is paying off. (The Principal)

Mark paid $32.28 of the $400 he owes. Mark paid $32.28 of the $400 he owes. $400 – = $ $400 – = $ $ is the new Balance he has to pay. $ is the new Balance he has to pay. Balance * Monthly Interest Rate Balance * Monthly Interest Rate $ * = $2.14 $ * = $2.14

The Second Month Mark pays $34.61 each month Mark pays $34.61 each month $34.61 $2.14 Goes toward Interest Goes toward the $ he is paying off. (The Principal)

Each month Mark pays off more of the Balance. Each month Mark pays off more of the Balance. The amount of money that goes toward the Principal is larger each month. The amount of money that goes toward the Principal is larger each month. The amount of money that goes toward the interest gets smaller each month. The amount of money that goes toward the interest gets smaller each month.

MonthBalancePrincipalInterestPayment

MonthBalancePrincipalInterestPayment

Here’s the big question: Here’s the big question: How do you figure out the equal monthly payments? (the $34.61) How do you figure out the equal monthly payments? (the $34.61)

You have to use a BEAST of an equation: You have to use a BEAST of an equation: P = Principal ($400) P = Principal ($400) J = Monthly Interest (Interest Rate / 12) J = Monthly Interest (Interest Rate / 12) N = Period of the loan (number of months) N = Period of the loan (number of months)

Here it is: Here it is: P * (J/ (1- (1+J)^-N)) $400 * ( / (1 – ( )^-12))