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Another Perspective on Amortization Schedules

Another way of viewing how interest is calculated when you borrow money is as follows.

Assume you borrow $10,000 from Bob and agree to pay 1% per month interest on the outstanding balance. Bob hands you the money and an interest clock starts ticking. You are paying Bob interest for the use of his money. One month later you owe Bob interest of 1% of $10,000 which is $100 plus the original loan of $10,000. If you pay Bob only $100 (interest only) then the outstanding balance remains at $10,000. If you pay Bob the $100 of interest and also give him $1000 then your outstanding balance owing to Bob is reduced to $9000. Notice the interest is calculated and paid FIRST. Your first payment total to Bob is $1100. Balance owing to Bob is $9000.

Next month comes along and you now owe Bob interest of 1% of $9000 which is $90 plus the outstanding balance of $9000. Lets assume you pay the $90 plus another $1000 thus the balance owing Bob is now $8000. But what if one minute later (after giving Bob the $90 plus the $1000) you decide to pay an additional amount of $2000 then the outstanding balance would be $6000. The extra $2000 could be thought of as a prepayment of principal. (you would never prepay interest as that would be ludicrous, by definition).

Your second payment total to Bob is $3,090. Balance owing to Bob is $6000.

Your third month comes along and you now owe Bob 1% of $6000 which is $60 plus the outstanding balance of $6000. You’re budget this month was severely attacked by your SEARS card thus you ask Bob to cut you some slack and let you skip this months interest payment and principal payment. Bob says OK! You still owe Bob the $60 in interest (for the use of the money) so it gets added to the outstanding balance, making the outstanding balance $6060. In banking terminology you have just entered into a negative amortization schedule because the outstanding balance has increased. Your third payment total to Bob was zero and balance owing to Bob is $6060.

Your fourth month comes along and now you owe Bob 1% of $6060 which is $60.60 plus the outstanding balance of $6060. NOTE! You have now started to pay compound interest by definition (interest on interest). The interest you paid prior to this was normal interest due for the use of Bobs money. You pay Bob the $60.60 in interest plus $3,060 towards the outstanding balance. By definition anything paid in excess of the interest owing automatically goes towards lowering the outstanding balance.

Your fourth payment total was $3,120.60 ($60.60+$3,060) and your balance owing (outstanding balance) to Bob is $3000.

Your fifth month comes along and YOU pay Bob the interest of $30 (1% of the $3000) plus the outstanding balance of $3000 and low and behold you have amortized or paid the loan in full.

This explanation is nothing more than an amortization schedule. The calculation of an amortization schedule is always performed the same way regardless of the type of interest factor. Do not confuse the words "compounding" and "calculation". They DO NOT mean the same thing! This particular example happens to be a 12% annual interest rate with “monthly compounding” thus the monthly interest factor is 0.12 / 12 = 0.01 which made the mathematics easy to visualize. It was purposely chosen because most monthly payment American mortgages and monthly payment, non collateral, Canadian mortgages (and also personal loans in Canada and the USA) utilize this type of interest factor for monthly payment loans. The mathematics for a loan or a mortgages is identical. A mortgage is just a special name of a loan.

 

To calculate the monthly interest factor for a monthly payment mortgage using "monthly compounding" the formula is

i = R/12

"i" is the monthly interest factor and "R" is the annual interest rate.

To calculate the monthly interest factor for a Canadian mortgage utilizing "semi-annual compounding" the formula is

i = {(1 + R/2)^(1/6)} - 1

In plain english, this means divide the annual interest rate (as a decimal) by 2 and then add 1. Raise the result to the 1/6th power and then subtract 1.

Using the 12% rate example.

1.06 to the 1/6th power minus 1 gives

a Canadian monthly interest factor of 0.0097587942 which is less than the monthly compounding factor of 0.01 used in the example above.

 

 


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