­

## Effective Interest Rate Example

• Vm = The Value of the Mortgage

• Rm = The Rate of the Mortgage (also called the mortgage constant)

• Ym = Yield of the Mortgage (also called the interest rate or the return on investment)

• Vo = Value of the Property

• ADS = Annual Debt Service (the amount of the total yearly payments on the mortgage)

• n = Term of the loan (the length of time that the mortgage is amortized)

• b = balloon payment or loan balance due. A balloon refers to the remaining balance amount of a loan that comes due in one large sum at a specified time in the future.

• M = Loan-to-Value ratio (amount of money lent divided by total value of property, Vm/Vo)

• Ve = Value of the Equity (the amount of equity in the property which is the total value of the property minus any existing mortgage loans)

• Points = Points on a loan refers to the extra charge assessed by the lender to process the loan application and provide the funds. This is in addition to the interest payments made on the loan. One point is equal to 1% of the total amount of the loan given. For example, a \$50,000 mortgage loan that has 3 points. The total amount the borrower has to pay for the points is \$50,000 x 3% = \$1,500

• Amortization = The monthly payment schedule to gradually pay off the loan balance of principal plus interest over a specified period of time.

Let's take an example so we can put all these abbreviations to work:

• Vm = \$100,000

• Ym = 12%

• n = 20 years

• Points = 6

Six points are equal to 6 x 1% = .06

.06 x \$100,000 = \$6,000

\$100,000 - \$6,000 = \$94,000

This tells us that the borrower has to pay back \$100,000 but he actually only receives \$94,000 from the lender. The \$6,000 is kept by the lender to pay for the points on the loan.

• ADS = Vm x Ym which in this equation would be \$100,000 x 12% = \$12,000

\$12,000/\$100,000 = .12 or 12%

\$12,000/\$94,000 = .1277 or 12.77%

Therefore, the contract interest rate for this loan is 12% but the effective interest rate for this loan is 12.77%. This simply means, that due to the additional cost for the loan points, the actual interest rate that the borrower is being charged for the money is 12.77% and not just 12%. This is why all loan agreements state the effective interest rate at the top of the loan document. By doing this, the borrower can see the full amount of interest, and the total of all of the payments, that they are being held responsible for.

Nominal interest rate is the annual rate charged for a loan and it's the same thing as the contract interest rate. It's just another phrase used to describe what the interest rate is that's stated in the loan contract.

The monthly effective interest rate charged for the loan is the effective rate divided by 12.

.1277/12 = .0106   or   1%