Step by step
The question
Question: A student loan of $25000 at 6.6% for 10 years is paid monthly.
Find the monthly payment and the total interest.
1 Read the numbers
P is the money borrowed: $25000.
r is the yearly rate: 6.6% is 0.066.
n is how many times a year: 12.
t is the time: 10 years.
2 Per payment
Interest is added each month.
The rate for one month is i: r over n.
0.066 divided by 12 is 0.0055.
And N is how many payments: 12 times 10 is 120.
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 0.0055 is 1.0055.
4 Work it out
The top: 137.5.
With a calculator, 1.0055 to the power negative 120 is about 0.517787.
1 minus that is 0.482213.
Now the top over the bottom.
137.5 divided by 0.482213 is 285.1436 and a bit.
Lenders round up to the next cent: 285 dollars and 15 cents a month.
Careful!
That pays back only the loan.
The interest must be paid too.
5 Total interest
120 payments of 285 dollars and 15 cents: $34218 in all.
The interest is what is paid on top of the loan: $9218.
6 Check
Let's check with the first month.
The interest that month is 25000 times 0.0055: 137 dollars and 50 cents.
The rest of the payment, 147 dollars and 65 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.