# APR without principal repayment?

I've been trying to find out about this own my own but can't seem to work it out via search engines, loan/mortgage websites and excel.

When I try to work out how much a loan costs, rates like APR seem to ask for monthly payment or no. of payments. AND when they work out or use "payment", they include both the capital repayment and the interest (+fees).

Is there a term that describes Percentage rate that constitutes interest and fees of the loan but not the loan amount itself EDIT: more like "principal amount"? i.e. a percentage of your "out of pocket" expense not including the money you borrowed which i think better reflects the cost of a loan.

With most loans in the US, you get what is called an amortization schedule which shows how each (monthly) payment gets divided into capital repayment and interest+fees. The monthly payment is fixed; it is the same amount month after month. But, the breakdown of the payment into capital repayment and interest payment differs from month to month as earlier payments are mostly interest and later payments are mostly capital repayment. This is because each month the money still owing goes down and so the interest for next month is less. With a fixed monthly payment, next month's interest is a little less and capital repayment is a little more. In this scenario, if the total of the many monthly payments is \$X and you borrowed \$Y to start with, then your total cost of borrowing money is simply \$(X-Y). What interest rate did you pay for borrowing the money? It is the APR divided by 12 per month. That is, if you borrowed \$1000 at 6%APR compounded monthly, then you owe \$1000x0.5% = \$5 in interest at the end of the first month. If the loan is for 5 years (60 equal monthly payments), you pay \$19.33 each month. In the first month, you have paid \$5 in interest and reduced the principal due by \$14.33 (that is, you owe only \$985.67). So next month you owe only \$4.93 = \$985.67x0.5% in interest, but since the monthly payment is still fixed at \$19.33, you get to pay off \$14.40 (a tad more than last month's \$14.33) of the amount still outstanding. Lather, rinse and repeat until your 60th payment of \$19.33 consists of \$19.23 of principal finally being paid off together with 10 cents interest for that last month on that \$19.23 you still owed. You will have paid \$19.33x60 = \$1159.80 in monthly payments, that is, \$159.80 in interest over the life of the loan. If you want to think of it as 15.98% interest over 5 years or a shade under 3.2% per year, feel free to do so. However, most people won't think of it that way, because they didn't have the use of the full \$1000 for the entire 60 month period. Note that there is no compounding of interest, that is, you are not charged interest on previously accrued interest because you are paying off the interest in full each month.

It is also possible to get interest-only loans where each month you only pay the interest (and the fees) accrued that month. At the end, the entire loan amount is due (usually called a balloon payment). Note that the monthly payment is fixed in this instance too. Thus, you pay \$5 interest each month and at the end of the loan period, you owe the full \$1000 since you have not repaid any part of it. In fact, your last payment would be \$1005 consisting of the interest for that last month plus the full principal amount. Note that there is no compounding of interest, that is, you are not charged interest on previously accrued interest even though there is no repayment of any part of the principal over the entire life of the loan.

Hybrids of these two types of arrangement such as "pay the interest and fees each month plus \$20 towards the principal" are also possible. This would pay off our example loan of \$1000 in 50 months instead of 60. Note that each month's payment would be smaller than the previous month's payment because the amount of interest charged each month is decreasing by \$20x0.5% = 10 cents each month.

But note that in all these cases, the percentage interest you pay each month is still the same APR/12. What differs in the three cases is what the interest is being charged on. And it is all simple interest, not compound interest, that is charged. The phrase "6% APR compounded monthly" merely means that you pay 0.5% per month simple interest on the remaining balance. If it said "compounded quarterly" and you were making quarterly instead if monthly payments, you would pay 1.5% per quarter, and it would still be simple interest each quarter on the remaining balance.

In a different scenario, if you lend money to a bank (this is usually called a Certificate of Deposit or CD) for 5 years at 6% APR compounded quarterly (that's what my bank offers instead of monthly compounding -- your bank might be different), then the interest is compounded and at the end of 5 years (20 quarters) when the CD matures, you will get

\$1000 x (1 + 0.015)^20 = \$1346.86

The compounding has increased the interest that you have earned from 6% x 5 = 30% to 34.686% which is 6.136% compounded annually or, if you like to think about it differently, you got 34.686%/5 = 6.937% simple interest per annum. (Most everyone else will beg to differ, but whatever makes you comfortable).
This is how CDs work in the US. In India, CDs are commonly called FDs (Fixed Deposits) and the interest accrued is paid out quarterly (or monthly depending on the way it is set up) to the owner; that is, interest does not accumulate inside the CD as it does in the US (hence Fixed Deposit), and it is all simple interest: no compounding since it is all paid out. You would get 1.5% per quarter (\$15) for a total of \$300 instead of the \$346.86 that compounding would give you (but only after 5 years). But, getting back to the US, interest earned inside a CD must be declared annually as income and the bank will include it in the 1099-INT that it sends you (and the IRS), and you have to pay tax on that money from other assets or income since you won't have that cash in hand till the CD matures.

• Thanks for your elaborate answer. I am definitely talking first scenario. Is the amortization calculable and fixed or are the lenders free to fiddle with the schedule as they see fit (before actually lending)? Apr 26, 2014 at 1:09
• I think what I missed was the fact that the interest rate is compounded and to work out new principal on which to be charged interest next, principal repayment is obviously needed. please conclude your answer with this so that people will know how it actually answered my question and i'll accept your answer Apr 26, 2014 at 1:31
• Amortization schedules should be the same in all cases; and calculators are available widely on the Internet. However, sometimes games are played with fees etc. For example, mortgage payments are usually due on the first of the month. If the closing is in the middle of April, the first payment is due on June 1 (for interest accrued May 1 - May 31), and you have the option of pre-paying interest for the remainder of April, or have that April interest tacked on to the principal amount (lender will suggest this). Apr 26, 2014 at 1:55
• I have no idea what is meant by interest being compounded. You pay simple interest on the amount still owed, and since you pay off the interest each month, there is no compounding of interest, that is, no interest is charged on the interest. See also this question. Apr 26, 2014 at 2:03
• ok, not exactly compounded but recalculated every month. Apr 26, 2014 at 12:28

4 years and 7 months later, looking back at the question, the term i think I was looking for is "Cost of Loan"