# How to Calculate the Effective Interest Rate Including Discount Points

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Effective interest rate is the amount of money that a borrower pays for a loan in one year expressed as a percentage. The effective interest rate is sometimes called the annual percentage rate, or APR, with home mortgages. The APR takes into account all costs that the buyer pays in order to secure the loan, and it can vary considerably between loan packages. To compare the true cost of several loans, it is helpful to compute the APR for each loan, and then compare each APR.

## With a Financial Calculator

List the advance fees charged in order to obtain the loan. These fees include origination fees and application fees, as well as mortgage insurance premiums paid in advance. Include discount points as well. One discount point equals 1 percent of the loan value. Add together all of these advance costs.

Use a financial calculator to determine the payment of the loan without advance fees (see Resources). Enter each of the known values, except for payment, and use the calculator to determine payment. Many financial calculators require you to enter the interest rate per period, so divide the stated interest by 12.

Subtract the total amount of points from the principal amount of the loan. Enter that amount under the present value field in the financial calculator. Calculate the interest per period using this new principal amount. Multiply the interest per period by 12. Add to that amount the percentage rate per month that you must pay in private mortgage insurance, and the result is the APR, or effective interest rate.

## Without a Financial Calculator

Calculate the amount of interest paid in one year using simple interest. Multiply the amount of the loan by the stated interest rate. On a \$100,000 loan at 7 percent, this would be \$7,000, or 7 percent multiplied by \$100,000.

Subtract the amount of any advance fees from the loan amount. If the \$100,000 loan has \$3,400 in advance fees including points and origination fees, the difference between these two would be \$96,600. This is the amount of money that you actually have use of with this loan, or the loan proceeds.

Divide the total interest paid by the amount of the loan less the loan proceeds. This, added to the percentage of mortgage insurance charged per month, will give an approximate APR for one year. In the case of our example, the APR for one year would be 7.24 percent, or \$7,000 divided by \$96,600. This is not the true APR over the term of the loan, as this amount only reflects the APR for one year. However, this calculation is useful for a quick comparison if a financial calculator is not available.

#### Tips

• You may also figure the amount of tax advantages you receive from a mortgage when calculating the effective rate. Add the amount of tax savings in a year to the loan proceeds before completing the calculation. The tax savings is like borrowing additional money that you do not pay any more interest on.

#### Warnings

• Some people consider the effective interest rate to be the amount expressed as a percentage of the total interest actually paid in a year divided by the amount borrowed. This takes into account that each payment made reduces the principal, and therefore the interest charged each period. On longer-term loans like mortgages this has minimal effect, and makes the calculation much more complicated.