What Is the Formula Used to Calculate Loans?


When you take out a loan from a commercial lender, you are paying a premium in order to borrow the money. To help you determine whether you can afford the loan and whether it will be worth it to borrow the money, you can use several formulas to determine how much the loan will cost you, both in monthly payments and over time. If you are taking out a mortgage and are deducting the interest from your taxes, you can also use formulas to determine how much of your payments go toward interest.

Determining Monthly Payments

The most common formula used for loans is one that determines monthly payments. Use the formula below where MP is the monthly payment, P is the principal, R is the monthly interest rate and L is the length of the loan in months. If you have the annual interest rate, divide it by 12 to get the monthly interest rate. MP = P * (R + (R / ( ( R + 1 ) ^ L - 1) ) ) For example, a loan of $220,000 at 5.5 percent annual interest over 30 years would have a monthly payment of $1,249.14.

Determining Interest Per Payment

Each time you make a payment on a loan, part of the payment goes toward accrued interest and part goes toward paying down the loan. To determine how much of the payment goes toward interest, use the formula below where P is the remaining principal and R is the annual rate. Interest Paid = P * R / 12 For example, if you owed $100,000 on your loan, $500 of your monthly payment would go to paying interest.

Determining Principal Per Payment

To determine how much of your monthly payment goes toward paying down principal, subtract the amount of interest you pay from your monthly payment. The remainder is the amount of the monthly payment that goes toward paying down your balance. Though your monthly payment remains the same, over time the amount that goes toward paying interest will fall and the amount that reduces principal will increase.

Effective Interest Rate

The interest rate of the mortgage will be lower than they interest rate you actually pay because interest is compounded more often than once a year. Most loans are compounded on a monthly basis. To calculate the interest rate you will actually pay, use the following formula where EIR is the effective interest rate, R is the stated interest rate and N is the number of times per year the interest is compounded. EIR = ( 1 + R / N ) ^ N - 1 For example, if you signed a mortgage at 6 percent compounded monthly, or 12 times per year, the effective interest rate would be 6.17 percent.

Loan Cost

In order to determine the amount of money that you pay over the life of the loan, multiply your monthly payment by the number of payments you have to make. To find the amount of money you will pay over the life of the loan, subtract the amount you borrowed minus the total cost of the loan.

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