Re: Interest calculations in TValue - Posted by Eduardo (OR)
Posted by Eduardo (OR) on April 15, 1999 at 21:30:10:
Actually, there are more than four possible methods (and more than four in common use) depending on how you define the parameters and and what you are trying to accomplish.
In computing simple interest, using a divisor of 360 days is called ordinary interest. When the divisor is 365 or 366, the result is know as exact interest.
And, there are two ways to compute the number of days between dates: Using all days except the first is called the exact method. Using 30 days for each month plus the exact number of days for a partial month is called the approximate method.
You can see there are now four ways to compute simple interest: 1. ordinary interest and exact time. 2. exact interest and exact time. 3. ordinary interest and approximate time. 4. exact interest and approximate time. The first (no. 1) is called Banker’s Rule. Banker’s Rule is the most common commercial practice.
Next we have common ways to charge interest on short-term transactions: Merchant’s Rule and United States Rule. With Merchant’s Rule, the entire debt earns interest to the final payoff date. Under U.S. Rule, the interest on the remaining principal balance is computed each time a partial payment is made.
With compound interest problems (as most mortgages are–they are calculated using compound interest methods although no “true” compounding is usually going on [interest is paid each time it’s charged] except in cases where the payment is less than interest-only), in the United States, interest is compounded periodically (usually monthly, although you can compound weekly, quarterly, annually, daily, or any other variation including "continuously) and the payments usually coincide (monthly compounding/monthly payments, weekly compounding/weekly payments and so on. In Canada, mortgages are often computed with bi-annual–twice a year (not to be confused with bi-ennial–once every two years)–interest compounding and monthly payments. In England, you have annual compounding and monthly payments. The common practice with mortgages in these countries, as you can see, is for the compounding period and the payment period not to coincide (they pay less than we do–fewer compounding periods).
Don’t forget, in your calculations, to keep straight the difference between effective interest rates and nominal interest rates. In an owner-carry real estate transaction of, say, $100,000, at 10% interest, amortized over 30 years, with monthly paysments, what we are really saying is that the annual rate of interest to be used in calculating the monthly payment, namely 10%, is a nominal or “named” rate because when you compound 12 times a year you end up with a different amount (12 times the monthly payment equals more than one times the yearly payment if you were compounding annually) than if you were compounding once a year. You can thus calculate the “real” or effective rate of interest which will be higher than the nominal rate because of the more frequent compounding.
Add-on interest loans are common in consumer lending. The Rule of 78 is one. This method allocates interest differently than the compound interest or annuity method used in morgages. It is often more costly for the consumer. I won’t go into the details.
But, you should also keep in mind the difference between simple ordinary annuities (an annuity, by definition, is a series of equal payments–such as a mortgage) and simple annuities due. Ordinary annuities have the payment at the end of each period (mortgages), annuities due have the payment at the beginning of each period (leases).
The compound interest method of amortization (mortgages–as opposed to, say, car loans [Rule of 78]) is also called the actuarial method.
Good luck. I can give you some references to textbooks if you want.