Interest Accruing Loan
The following example of an interest accruing loan was purposely chosen even though the interest rate is high compared to the current rates in 2004. This particular example was used extensively by the mortgage brokers section of the Ontario Ministry of Finance in 1992. It is easier for a novice to follow the same example set out in the governments publications. Once the concepts are understood then any rate or principal can be used in full confidence.
A mortgage with a face value of $45,000 is written up with an annual interest rate of 12% utilizing “semi-annual compounding, not in advance”. The loan is to be repaid in three years. No payments of principal or interest are to be paid during the three years. At the end of three years the outstanding principal and interest will be repaid in one payment. The total cost of all the fees relating to the loan is $3500.
QUESTION: What is the effective interest rate of this loan?
ANSWER: Just about any financial calculator could be used to solve this problem providing you are capable of calculating the semi-annual compounding, monthly, interest factor, i.
Where: i = [(1+R/2)^(1/6)] – 1 and R = the annual interest rate
i = 0.009758794 and the ^ operator is the exponent operator
or you could use the MORTGAGE2 PRO, Utilities Menu and select, Interest Factors,
As previously stated, any financial calculator that allows Present Value / Future Value calculations would allow one to calculate the Future Value (FV) of $63,833.35. A negative amortization schedule would calculate the same FV number. The advantage of the negative amortization schedule is, it is a continuous grid of Future Values.
The actual present value is $45,000 minus the $3,500 total fees that are paid up front (in the present). Thus;
The effective interest rate of this interest accruing loan is 15.43% because the $3500 fees were paid up front.
The Number of Periods, entered as years (3) makes by definition the new calculated interest rate the effective interest rate, In other words, the intrinsic property of any PV/FV financial calculator is, … if the number of periods is entered as years then the calculated interest rate is always the effective interest rate. There is no need to be concerned about the type of compounding when the period is yearly.
It is interesting to note, in Ontario, Canada the 15.43% number is called the Total Cost of Borrowing.