# Formula for calculating the total interest payable over the life of a loan

wondering if someone can help a non-mathematician out.

I am looking for the formula for calculating the total interest payable over the life of a loan.

Given that we know:

P: Principal (amount) of loan

R: The monthly repayments on the loan

T: The term of the loan (i.e. the number of repayments)

r: The annual interest rate


Assume that interest is accrued monthly and that repayments are made in arrears (at the end of each loan period).

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If you know the monthly payment and the number of payments, the total of payments is $RT$, so the total interest you pay is $RT-P$. The fact that the interest is accrued monthly and payments are made in arrears only go into calculating the payment from the interest rate, which has already been done for us.

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"If you know the monthly payment and the number of payments, the total of payments is RT, so the total interest you pay is RT−P. The fact that the interest is accrued monthly and payments are made in arrears only go into calculating the payment from the interest rate, which has already been done for us."

Part of Ross's answer must be missing, otherwise it makes no sense.

RT-P. Let's say R, monthly payments on loan, are \$1,000. T, total number of payments is 36. RT then equals 36,000, minus the Principal, which is \$36,000 = \$0. So, you're paying$0 in interest, and you've factored in the interest rate nowhere. Great!

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What makes you think that the principal is \\$36,000? That's only true if you implicitly assume that you are paying no interest. –  Nick Peterson Oct 28 '13 at 21:13
You don't need the interest rate to calculate this. You may not have a calculated interest rate even and this formula would apply. FYI, your "answer" should have been posted as a comment to Ross' (correct) answer, not as a separate answer. –  Jared Jul 4 at 23:22