Mortgage calculations

Several types of mortgage calculation questions appear on the exam. Here are some examples:

Example 1: What is the first year's interest on a mortgage for $200,000 at 6% interest for 30 years?

Unless otherwise stated, interest is always assumed to be annual. For this type of question, the entire balance is considered to be outstanding in the first year (or an interest-only loan). The term of the mortgage doesn't matter. So,

$200,000 (Amount of Mortgage) x 0.06 (Interest Rate) = $12,000 (Interest Due the First Year)

Example 2: Using the figures in the previous example, if the loan is an amortized loan, how much interest is due the first month?

$12,000 (First Year's Interest) ÷ 12 months = $1,000 (Interest Due the First Month)

Example 3: Using the information in the previous example, assuming that the monthly payment is $1,300, what is the balance owed on the mortgage after the first month's payment is made?

$1,300 (Total Payment) - $1,000 (Interest) = $300 (Principal Paid)

$200,000 (Original Mortgage Amount) - $300 (First Month's Principal Payment) = $199,700 (Balance)

Remember: In an amortized mortgage, each payment is made up of principal and interest.

Another common mortgage question asks you to calculate the amount necessary to amortize (or pay off) a certain amount of mortgage at a certain interest rate for a certain term given a monthly payment of a certain amount per $1,000 of mortgage.

Example 4: A 20-year mortgage at 5.5% carries a monthly payment of $6.60 per thousand. What is the total monthly payment for a $275,000 mortgage?

$275,000 ÷ $1,000 = 275 units of $1,000 each

275 x $6.60 (Payment per Thousand) = $1,815 per month

Proration

Proration problems sometimes appear on real estate exams, depending if it is common in your area to close title through an escrow agent or in a face-to-face closing. The theory of proration is quite simple, and understanding the theory helps you understand the math.

Taxes (or any other costs, such as homeowners' association fees) are paid either in advance or in arrears for a certain period of time. In Florida, for example, taxes are paid in arrears in November for the entire year that is just ending. This means that the owner has used the property before he has paid the taxes for that period of use. Proration is simply reconciling the payment with the period of time that the property was used. Florida uses a 365-day year to divide the taxes between the buyer and seller, and the buyer is charged for the taxes on the day of closing.

Example 1: Taxes of $1,788.50 are paid in arrears on November 10 for the year. Closing occurs on December 10. What is the tax proration?

$1,788.50 ÷ 365 days = $4.90 per day

Counting from the date of closing, the new owner will own the house for 22 days and, therefore, she'll owe the seller 22 days' worth of taxes.

22 days x $4.90 per day = $107.80

In proration terminology, the seller gets a credit of $107.80, and the buyer gets a debit of $107.80.

Example 2: Let's say homeowners' association fees are paid in advance at the beginning of the month. To keep it simple, we'll say that they are $300 and the closing on the property is June 20 (June is a 30-day month). Assuming that the buyer is charged for the day of closing, who owes how much to whom?

$300 ÷ 30 days = $10 per day

The seller has already paid the full amount, but the buyer will own the property for 11 days.

11 days x $10 per day = $110 (Amount the Buyer Owes the Seller)

Note: For exam purposes, the terms tax year and fiscal year may be used interchangeably.