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1 How Interest Is Computed As Time Goes By Checklist The Loan Payment Amortizing the Loan Amortize the Loan Some More

2 When you calculate a loan payment you are determining what periodic payment a borrower must make to pay all or part of a loan back to the lender. But how about during the life of the loan? What is happening to that loan as it is being paid back? Unless the payments are for interest only, the borrower is slowly but surely reducing the indebtedness owed to the lender. Of course, not all of the payment, in almost all cases, is being applied to pay down the principal, that is, the amount owed the lender. Some of the money - often a lot of the loan payment! - is applied to interest, the cost of borrowing the money. What we are going to do in this section is calculate these figures, how much is going to interest, to principal, and what the loan balance is at any one time. HOW INTEREST IS COMPUTED: First, let s figure out a loan payment. Say we have a \$150,000. loan at % annual interest over a loan term of 30 years payable on a monthly basis. What that means is that % of the loan balance will be charged annually for the interest. Actually, for a loan that is paid more frequently than annually, the interest is going to turn out to be less than % of the starting loan amount. The reason for that is that interest is charged on the loan balance and as that balance declines, that is, as portions of the loan payments are applied to reducing the principal amount owed, the % is applied to the reduced loan amount still outstanding. Look at the interest that will be due on this loan for the first of the 360 payments (12 months a year times 30 years): \$150,000. x.0 \$ 13,500. Divide 12 months per year into the annualized interest of \$13,500. to get \$1,125. Keystrokes Algebraic: x % 12 = Answer: 1, RPN: ENTER % 12 Answer: 1, So, for the first month \$1,125. of the loan payment will be applied to interest and the remainder of the loan payment, which we figure below, will go to paying down the principal. The interest for the second month is then calculated on the loan balance having been reduced by the portion applied to principal from the first month s payment. This balance will be multiplied by %, the result will be divided by 12 months to figure out the second month s interest and the remainder of the loan payment applied to the principal loan balance. AS TIME GOES BY: A little bit less is applied to interest for the second month compared to that applied to interest for the first month because the % interest is taken of a loan balance in the second month that is slightly less than the starting amount of the loan that was used to calculate the first month s interest. Hence, slightly more is applied to principal for the second month from that constant loan payment. In this way, over the life of a loan, less and less is applied to interest and more and more is applied to principal the longer the loan is held. hp calculators - 2 -

5 Note that these amortization figures are just for payments 85 through 168 and do not include the interest and principal paid during the first 84 payments. Of course, the balance figure of \$122,52.83 is what is still owed on the loan after the borrower has paid 168 payments. You can amortize over any range of payments. So, after the first 84 payments, instead of amortizing the next 84 by pressing NEXT, we could have just amortized the next year of payments by pressing 12, the next 2 years by pressing 24, whatever range of payments you want. hp calculators - 5 -

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