## Cost of Borrowing Explained

Total Cost of Borrowing

What does it mean? Before that question can be answered you must understand how a SIMPLE amortization schedule is calculated.

Assume you borrowed \$1000 for one year at 12% from a friend and agree to pay it back in 12 monthly payments of \$88.85. You might think at the end of the year you would have paid your friend back the loan plus \$120 is interest (.12 x 1000 = \$120). You can see that an ordinary amortization schedule

would prove at the end of the year your friend would only have made \$66.18 in interest. The only way your friend can make at least the \$120 in interest is if he lends out your payments each month as he receives them at the same interest rate he is charging you, to someone else. You see from the negative amortization schedule

that your friend will actually make \$126.83 in interest if he reinvests each monthly payment at the same interest rate. The extra interest of \$6.83 is because of the COMPOUND interest he is earning by reinvesting your monthly payments.

The 12% is called the Annual Interest Rate (AIR).
The 12.6825% is called the Effective Interest Rate (EIR) which is the effective rate the lender achieves if the payments are invested out at the same interest rate each month at the same rate.

Let’s assume your friend decides to charge you the \$10 it cost him to acquire the amortization schedule before giving you the \$1000. You tell him OK, and to just give you \$990 instead of \$1000. What is your new AIR now because of this fee?

In essence you are making monthly payments of \$88.85 based upon borrowing \$1000 at 12% but now you’re only getting \$990. A mathematical technique is to calculate what interest rate would satisfy the amortization formula for a \$990 loan for 12 payments of \$88.85? The answer is 13.92%.

The new AIR is 13.92% and the corresponding EIR is 14.84%
The new AIR or the new EIR are often called the TOTAL COST of BORROWING or THE COST OF BORROWING. You need to check with the local state (Americans) and provincial laws (Canada) as to which number they make the brokers quote as the cost of borrowing or the total cost of borrowing.