Monthly payments

Question

You want to buy a $27,000 car. You can make a 10% down payment, and will finance the balance with a 4% interest rate for 48 months (4 years). What will your monthly payments be?

Answer 1

The following formula will calculate the monthly payment of any fixed rate loan.

Payment = Principal * (r/n)

1 - [ 1+ (r/n)] ^-nt where n is the number of payments in a year, t is the number of years,

r is the interest rate, P is the amount of the loan.

We know that the principal will be 27,000 - 2,700 or 24,300

The rate is 4% or .04

n is the number of payments in a year, so that is 12.

Here we go Payment = 24300(.04/12)

1 - [ (1 + .04/12)^-4*12]

=. ______81______

1 - [ 1.003333^-48]

= 81

1 - [ 0.85238)

= 81

0.147629

= $548.67

Answer 2

27,000*10% = 2,700

27,000 - 2,700 = 24,300 ( the amount to be financed)

Using a financial calculator, the monthly payments will be $548.67

Here is the formula in case you don't have a financial calculator handy:

Loan payments =

Principal÷ {[ ( 1 + r/n )^t*n ] - 1 } ÷ [ (r/n) ( 1 + (r/n))^t*n]}

Where r is the annual interest rate (4% = 0.04 in this case), n is the number of payments per year (12 in this case, since the payments are monthly), and t is the number of years (4 in this case).

Note that t*n = 4*12 = 48 in this case. In other words, there are 48 monthly payments. The monthly interest rate is 0.04/12, but that does not have a nice non-repeating decimal value.

Computer spreadsheets usually have a function like this. EXCEL definitely does: PMT.

You could also use a spreadsheet and insert the above as a formula. That would be especially helpful if you had several such problems which differed only in the interest rate, principal, payment frequency, and loan length (time).