Step by step
The question
Question: A car loan of $22000 at 2.4% for 4 years is paid monthly.
Find the monthly payment and the total interest.
1 Read the numbers
P is the money borrowed: $22000.
r is the yearly rate: 2.4% is 0.024.
n is how many times a year: 12.
t is the time: 4 years.
2 Per payment
Interest is added each month.
The rate for one month is i: r over n.
0.024 divided by 12 is 0.002.
And N is how many payments: 12 times 4 is 48.
3 Use the formula
The payment each month: PMT = P times i, over 1 minus (1 + i) to the power negative N.
We put the numbers in: 1 plus 0.002 is 1.002.
4 Work it out
The top: 44.
With a calculator, 1.002 to the power negative 48 is about 0.908551.
1 minus that is 0.0914489.
Now the top over the bottom.
44 divided by 0.0914489 is 481.1431 and a bit.
Lenders round up to the next cent: 481 dollars and 15 cents a month.
Careful!
That pays back only the loan.
The interest must be paid too.
5 Total interest
48 payments of 481 dollars and 15 cents: 23095 dollars and 20 cents in all.
The interest is what is paid on top of the loan: 1095 dollars and 20 cents.
6 Check
Let's check with the first month.
The interest that month is 22000 times 0.002: $44.
The rest of the payment, 437 dollars and 15 cents, pays the loan down.
So the loan gets smaller every month.
It makes sense!
Let's look back.
First: read the numbers.
Then: per payment.
Then: use the formula.
Then: work it out.
Then: total interest.
Last: check.