Compound Interest & Mortgages

Simple Interest

Simple interest implies that interest is charged, due and payable, only once during the life of the debt, and at the end of the term. As such, if you borrow $100,0000 at 10% per annum for five years you will owe 50% at the end of year five, or $50,000.

Compound Interest

If the lender asks you to pay this $50,000 in equal annual installments of $10,000 this then becomes compound interest. The reason is that you are forced to part with your money early, i.e. before the end of the five year term. As such, you will lose the ability to earn interest on this money were you able to invest it until the end of year five. Similarly the lender gains the benefit of being able to invest the annual sums repaid and earn additional interest.

In examining the above charts you will notice that the only real difference between compound and simple interest is the frequency that interest payments are due. In both cases the Total Interest Paid figure is $50,000 however when compounded you are asked to pay the interest periodically during the course of the loan.

Consider that if the lender reinvests the yearly interest payments of $10,000 at 10% p/a until term end they will earn an additional $11,051 of interest. Therefore total interest received is, $50,000 plus $11,051 = $61,051. Similarly the borrower loses the use of these funds after the amounts are paid and foregoes the opportunity to earn this $11,051 interest. This is interest earned on interest, and therefor compounded, even though it is not an accruing loan.

If this were an interest accruing loan, one where the interest payments due go unpaid and are added to the principal amount owing each year, the balance in five years would be $161,051. The total interest paid is then $61,051, same as the compound interest example with the periodic payments reinvested.

Compounding is the earning of interest on interest

For interest accruing loans the earning of interest on interest is explicitly apparent as interest due is added to the principal amount outstanding and earns interest itself in subsequent periods. Compounding loans that are not interest accruing still earn interest on interest due to the presumed reinvest of the periodic interest payments to earn additional interest.

The above example explains why mortgage interest is compounded even though mortgages are not interest accruing loans. Remember that mortgage interest due each month is never added to the principal amount, it is always paid when due along with a principal amount sufficient to amortize the debt. Unless, of course, the borrower is in default of payment.

Mortgages

Mortgage loans are calculated to be paid off within a specified period of time through the regular repayment of the principal outstanding. Each monthly installment results in the repayment of part of the outstanding balance. This balance is therefore lowered and subsequent interest charges decline accordingly.

Notice that the sum of payments each year is fixed at $10,734. In the first year the principal portion is only $979 and the remainder of the constant payment goes towards interest owed. As the balance declines the interest owed is reduced so that the interest payment constitutes a smaller portion of the constant payment. More and more of this payment is applied to the repayment of the outstanding balance each month until the loan is fully paid off (amortized).

$100,000 @ 10% Interest - Compounded Semi Annually and not in advance - 25 Year Amortization

The exact amount of the payment sufficient to pay off the loan is based on several factors including the pay back period (amortization), interest rate, and the loan amount. Most Canadian mortgages are "partially amortized" meaning that there is a fixed term at the end of which the outstanding balance is due. The payment is still calculated based on a full amortization period, say 25 years, but the mortgage contract with the lender extends for a shorter period. This period is called the mortgage term and can be 6 months to 10 years. At the end of the term the loan has been partially repaid (amortized). The balance outstanding is now due and can either be paid in full or the mortgage can be renewed, at then current rates and terms.

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