Analyzing Fixed Rate Loans

The most common loan analysis is the calculation of the periodic payment when the loan amount, life, and interest rate are known. The following PROC LOAN statements analyze a 15-year (180 monthly payments) fixed rate loan for \$100,000 with an annual nominal interest rate of 7.5%:

```   proc loan;
fixed amount=100000 rate=7.5 life=180;
run;
```

Another parameter the PROC LOAN statement can compute is the maximum amount you can borrow given the periodic payment you can afford and the rates available in the market. The following SAS statements analyze a loan for 180 monthly payments of \$900, with a nominal annual rate of 7.5%, and compute the maximum amount that can be borrowed:

```   proc loan;
fixed payment=900 rate=7.5 life=180;
run;
```

Assume that you want to borrow \$100,000 and can pay \$900 a month. You know that the lender charges a 7.5% nominal interest rate compounded monthly. To determine how long it will take you to pay off your debt, use the following statements:

```   proc loan;
fixed amount=100000 payment=900 rate=7.5;
run;
```

Sometimes, a loan is expressed in terms of the amount borrowed and the amount and number of periodic payments. In this case, you want to calculate the annual nominal rate charged on the loan to compare it to other alternatives. The following statements analyze a loan of \$100,000 paid in 180 monthly payments of \$800:

```   proc loan;
fixed amount=100000 payment=800 life=180;
run;
```

There are four basic parameters that define a loan: life (number of periodic payments), principal amount, interest rate, and the periodic payment amount. PROC LOAN calculates the missing parameter among these four. Loan analysis output includes a loan summary table and an amortization schedule.

You can use the START= and LABEL= options to enhance your output. The START= option specifies the date of loan initialization and dates all the output accordingly. The LABEL= specification is used to label all output that corresponds to a particular loan; it is especially useful when multiple loans are analyzed. For example, the preceding statements for the first fixed rate loan are revised to include the START= and LABEL= options as follows:

```proc loan start=1998:12;
fixed amount=100000 rate=7.5 life=180
label='BANK1, Fixed Rate';
run;
```

### Loan Summary Table

The loan summary table is produced by default and contains loan analysis information. It shows the principal amount, the costs at the time of loan initialization (down payment, discount points, and other loan initialization costs), the total payment and interest, the initial nominal and effective interest rates, payment and compounding intervals, the length of the loan in the time units specified, the start and end dates (if specified), a list of nominal and effective interest rates, and periodic payments throughout the life of the loan.

Figure 17.1 shows the loan summary table for the fixed rate loan labeled "BANK1, Fixed Rate."

Figure 17.1 Fixed Rate Loan Summary
The LOAN Procedure

Fixed Rate Loan Summary

BANK1, Fixed Rate
Downpayment 0.00 Principal Amount 100000.00
Initialization 0.00 Points 0.00
Total Interest 66862.61 Nominal Rate 7.5000%
Total Payment 166862.61 Effective Rate 7.7633%
Pay Interval MONTHLY Compounding MONTHLY
No. of Payments 180 No. of Compoundings 180
Start Date DEC1998 End Date DEC2013

Rates and Payments for BANK1, Fixed Rate
Date Nominal Rate Effective Rate Payment
DEC1998 7.5000% 7.7633% 927.01

The loan is initialized in December 1998 and paid off in December 2013. The monthly payment is calculated to be \$927.01, and the effective interest rate is 7.7633%. Over the 15 years, \$66,862.61 is paid for interest charges on the loan.