Step by step
The question
Question: A mortgage of $120000 at 4.8% for 25 years is paid monthly.
Find the monthly payment and the total interest.
1 Read the numbers
P is the money borrowed: $120000.
r is the yearly rate: 4.8% is 0.048.
n is how many times a year: 12.
t is the time: 25 years.
2 Per payment
Interest is added each month.
The rate for one month is i: r over n.
0.048 divided by 12 is 0.004.
And N is how many payments: 12 times 25 is 300.
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 0.004 is 1.004.
4 Work it out
The top: 480.
With a calculator, 1.004 to the power negative 300 is about 0.301916.
1 minus that is 0.698084.
Now the top over the bottom.
480 divided by 0.698084 is 687.5964 and a bit.
Lenders round up to the next cent: 687 dollars and 60 cents a month.
Careful!
That pays back only the loan.
The interest must be paid too.
5 Total interest
300 payments of 687 dollars and 60 cents: $206280 in all.
The interest is what is paid on top of the loan: $86280.
6 Check
Let's check with the first month.
The interest that month is 120000 times 0.004: $480.
The rest of the payment, 207 dollars and 60 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.