Financial Calculations Related to Lending

Instructor: Ian Lord

Ian has an MBA and is a real estate investor, former health professions educator, and Air Force veteran.

Loan shopping involves a number of financial calculations. In this lesson, we will look at some of the common formulas used when talking about qualifying for and paying down mortgages.

Financial Calculations in Lending

Fred is shopping for a mortgage on his new home, but since it's his first time buying a house, he's unsure of what all these numbers mean. Fred's mortgage broker, Bob, brings up a volley of terms like loan to value and APR, and starts running on about how the loan payments are calculated. Fred asks Bob for a layman's explanation of how that all works and how these amounts are figured. Let's take a look at how Fred's mortgage broker tries to explain these formulas and how they are calculated.

Loan to Value Ratio

Bob explains that in every mortgage the bank wants to know the ratio between what the property is worth and what the outstanding balance is on the loan. The loan to value ratio (LTV) allows lenders to easily visualize what the percentage of equity or principal stands against the mortgage amount. The formula looks like this:

LTV = mortgage balance / appraised property value

So if the house appraises and sells for $100,000 and Fred puts down $25,000 as a down payment, the mortgage is for $75,000. If we look at $75,000 over an an appraised property value of $100,000, we have an LTV of 75%. A 75% LTV means the house has 25% in equity.

The reason lenders care about the LTV is their risk of the borrower failing to make the payments. If the house is foreclosed on, the lender wants equity in the property so that it can sell the house for more than the remaining balance of the mortgage. The higher the LTV, the more risk the lender takes on.

Annual Percentage Rate

Fred sees something on the loan advertisement that confuses him a bit. Why does it say the interest rate is 4.2 and the APR is 5.506? Aren't annual percentage rate and interest rate the same thing? Not at all. The interest rate is set by the lender. The APR takes into account the total cost of financing over the life of the loan, which gives us an effective interest rate.

Mortgages have origination charges. Unlike a car loan, the borrower has to pay a fee to even get the loan. This fee is often rolled into the mortgage. Fred's mortgage has a $1,000 origination charge, but this amount can vary based on the lender and the particular loan. APR accounts for the compounding of interest and this additional fee. That $1,000 origination charge will be paid off a little bit each month plus interest for the entire 30 year duration of this loan. Here's one method of calculating the APR without using a financial calculator.

APR = (2 x number of payments per year x total finance charges) / (original loan proceeds x total number of payments + 1)

(2 X 12 X 57,795.10) / (76,000 X 360 +1)

(24 X 57,795.10) / (76,000 X 361)

1,387,082.4 / 27,436,000


APR = 5.056

Notice the APR is almost one percent higher. This is because that $1,000 origination fee has been rolled into the loan and then paid off over the 30 year life of the loan. Maybe Fred should consider paying that origination fee up front instead of taking an extra $1,000 on the loan!

Calculation of Loan Payment

Next Fred wants to know how his loan payment is calculated each month and what it will be. Bob shows him the following formula:

Mortgage payment = P { i(1 + i)^n } / { (1 + i)^n - 1 }

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