# 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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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!