Step by step
The question
Question: A personal loan of $4000 at 18% for 2 years is paid monthly.
Find the monthly payment and the total interest.
1 Read the numbers
P is the money borrowed: $4000.
r is the yearly rate: 18% is 0.18.
n is how many times a year: 12.
t is the time: 2 years.
2 Per payment
Interest is added each month.
The rate for one month is i: r over n.
0.18 divided by 12 is 0.015.
And N is how many payments: 12 times 2 is 24.
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 0.015 is 1.015.
4 Work it out
The top: 60.
With a calculator, 1.015 to the power negative 24 is about 0.699544.
1 minus that is 0.300456.
Now the top over the bottom.
60 divided by 0.300456 is 199.6964 and a bit.
Lenders round up to the next cent: 199 dollars and 70 cents a month.
Careful!
That pays back only the loan.
The interest must be paid too.
5 Total interest
24 payments of 199 dollars and 70 cents: 4792 dollars and 80 cents in all.
The interest is what is paid on top of the loan: 792 dollars and 80 cents.
6 Check
Let's check with the first month.
The interest that month is 4000 times 0.015: $60.
The rest of the payment, 139 dollars and 70 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.