A Bank is offering an interest rate of Prime less 2.25% for the first three months, then Prime (3.75%) less 0.375% for the remainder of the 6 year term. The APR is stated as 3.297%.
At first glance, one might be quick to congratulate the bank for its transparency and being forthright, because quoting the APR is intended to show the borrower the new effective interest rate because of the two different rates. Not so!
Ideally/realistically the bank should have used financial terminology that became law for mortgage brokers in Ontario in 1992, that is, the Total Cost of Borrowing (TCOB). In Ontario it is mandatory for mortgage brokers to show the total cost of borrowing (TCOB) for a loan as a single number that reflects all upfront fees/costs and any unusual changes or circumstances concerning a loan. In this case the TCOB is the phrase the bank should have used, not the American, APR terminology. This is not to be construed as anti Americanism, but just plain common sense that a bank should use the financial vernacular of the country or province where they conduct business. The bank did not mention the compounding method because when the APR or the TCOB is given, the type of compounding has already been factored into the APR or TCOB calculation. The loan officer verified the loan was calculated as per “monthly compounding”.
The calculations below based upon the well established principle, of present-value/future-value (PV/FV) calculations, show the TCOB/APR should be 3.408%. if one is being straight forward.
Annual Interest Rate (AIR) = 3.356%
Effective Interest Rate (EIR) = 3.408% ( > 3.356% due to “compounding”)
The 3.408% could have been calculated using a financial calculator in the PV/FV mode or one could have generated a negative amortization schedule using the MORTGAGE 2 PRO spreadsheet. Either method would have given 3.408% as the correct answer. Notice that the APR or the TCOB is just another name for the new effective interest rate.
According to the banks calculations the TCOB/APR for this loan is 3.297% . The 3.297% rate is understated and upon questioning the bank it was determined the bank calculated the APR as follows;
3/72 x 1.5% + 69/72 x 3.375% = 3.297%
The point that is begging to be made is as follows! A mortgage broker is required by law to use present-value/future-value calculations to calculate the correct value of 3.408% as the TCOB/APR yet this bank can use weighted average methods to arrive at a rate of 3.297% which is incorrect. If PV/FV mathematics is correct for mortgage brokers then why do the banks not have to follow the same rules? By the way the bank makes an extra $789 due to deemed reinvestment using the correct 3.408% instead of 3.297% over the six year term.
Had the bank been forthright they could have stated that their new wonderful “6 year flexible below prime mortgage” was equivalent to a monthly payment, monthly compounding loan with an annual interest rate of 3.356% (an effective interest rate of 3.408%).