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Calculating the Cost of Consumer Loans

Single-payment Loans: Lending institutions calculate interest on a single-payment loan using the simple-interest method.

With the simple-interest method, the principal and interest are due when the loan matures. Simple interest is equal to your principal (the amount you borrow) multiplied by your interest rate multiplied by the time (in years) that you hold the loan. If therer are no fees, your APR and your simple interest rate are the same.  The APR formula is:

[(Interest payments + fees)/number of years] / Average amount borrowed
For example, suppose you take out a $1,000 loan for one year for 12%. Assume you pay fees of $20 for a credit check and $20 for a processing fee.  Your interest rate is 12%. However, your APR = [($120 in interest + $40 in fees)/ 1 year] / 1,000 (your average amount borrowed) = 16%.
Now suppose this loan was for two years. Would your APR be different? The calculation would be:  APR = [($240 in interest + $40 in fees)/ 2 years] / 1,000 = 14%.  The APR is lower with a two year loan because you are allocating those $40 in fees between two years.

Home Equity Loans or Home Equity Lines of Credit: Home equity loans are generally either single-payment or installment loans. The benefit of these loans is that the interest may be tax deductible, reducing the cost of borrowing. The problem is that these loans will often keep people from making the hard financial choices to curb their spending. Why worry about spending when you can get a home equity loan or HELOC to pay it off? These loans sacrifice future financial flexibility and put your home at risk if you default.

Installment Loans: Installment loans are repaid at regular intervals; payment includes both principal and interest. Because of the complexity of this type of loan, it is best to calculate your payments using either a financial calculator or a spreadsheet program. Learning Tool 18: Credit Card Repayment Spreadsheet and Learning Tool 9: Debt Amortization and Prepayment Spreadsheet can help you determine your payments and interest costs. With these spreadsheets you can also calculate how long it will take to pay off a specific credit card or loan based on the balance owed, annual percentage rate, compounding periods, and payments per month. can help you calculate how long it will take to pay off your debt as well.

For example, assume the same $1,000 loan as above, but instead of a single-payment, we will pay for it monthly.  How do you calculate the APR for installment loans? The formula is the same. From your spreadsheet, I will build a simple loan amortization table from which you can calculate two different items: average amount borrowed and interest rate paid.
Simple Interest Method                                                                                      
                     Amount                         1,000    Stated Interest 12%                    
                     P/Y                                      12    PMT using Excel Function         
                     Years                    1                    Payment             $88.85                Remaining
                     Amount                Payment         Interest               Principal            Principal
1                $1,000.00                  $88.85                     10.00          $78.85                 $921.15
2                   $921.15                  $88.85                       9.21          $79.64                $841.51
3                   $841.51                  $88.85                       8.42          $80.43                $761.08
4                   $761.08                  $88.85                       7.61          $81.24                $679.84
5                   $679.84                  $88.85                       6.80          $82.05                $597.79
6                   $597.79                  $88.85                       5.98          $82.87                $514.92
7                   $514.92                  $88.85                       5.15          $83.70                $431.22
8                   $431.22                  $88.85                       4.31          $84.54                $346.68
9                   $346.68                  $88.85                       3.47          $85.38                $261.30
10                 $261.30                  $88.85                       2.61          $86.24                $175.07
11                 $175.07                  $88.85                       1.75          $87.10                  $87.97
12                 $87.97                    $88.85                       0.88          $87.97                   $0.00

Average = $551.55                Total Int.=                  66.19        

APR on interest payments alone = 12.0%

The total paid is $66.19 interest and $40 in fees divided by 1 year divided by $551.55, the average amount borrowed.  The APR is 19.3%.

Payday Loans: Payday loans are cash advances for a postdated check that the lender will cash on a specified day. The APR is equal to the simple interest paid over the life of the loan. The APR takes into account all costs for a year, including the interest rate, the cost of pulling credit reports, and all other fees; the total cost may be significant. To calculate the APR for any loan, multiply the amount of money paid in fees and interest by the number of periods in a year to get the annual cost of the loan; then divide the annual cost by the amount borrowed.

For example, suppose you paid $20 to borrow $100 for two weeks by writing a postdated check for $120. There are twenty-six two-week periods in a year. Thus the equation for finding your annual payment for this loan would be $20 * 26 = $520. In other words, you would pay $520 dollars in interest for a $100 loan: Consider that $520/$100 results in 520 percent interest. That is very expensive cash!  Do not use payday loans.

 



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