Step by step
The question
Question: A loan of $8000 at 9% for 3 years is paid monthly.
Find the monthly payment.
1 Read the numbers
P is the money borrowed: $8000.
r is the yearly rate: 9% is 0.09.
n is how many times a year: 12.
t is the time: 3 years.
2 Per payment
Interest is added each month.
The rate for one month is i: r over n.
0.09 divided by 12 is 0.0075.
And N is how many payments: 12 times 3 is 36.
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 0.0075 is 1.0075.
4 Work it out
The top: 60.
With a calculator, 1.0075 to the power negative 36 is about 0.764149.
1 minus that is 0.235851.
Now the top over the bottom.
60 divided by 0.235851 is 254.3979 and a bit.
Lenders round up to the next cent: 254 dollars and 40 cents a month.
Careful!
That pays back only the loan.
The interest must be paid too.
5 Check
Let's check with the first month.
The interest that month is 8000 times 0.0075: $60.
The rest of the payment, 194 dollars and 40 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.
Last: check.