##### Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) Prepare to review some of the math associated with mortgages. In these calculations, one important term to know is amortized loan, which means that each payment on the mortgage is a combination of principal and interest so that at the end of the mortgage term you have nothing left to pay.

How necessary is having a financial calculator for real estate work or for the state exam? A financial calculator is helpful and makes life easier if you know how to use it. As for the state exams, a simple inexpensive calculator does just fine. In fact, you can probably do most of the problems on your fingers and toes (if you have enough of them). © Brian A Jackson / Shutterstock.com

## How to Calculate Interest

A few standard problems that you may find on an exam deal with mortgage interest and principal payments. Here are the likely possibilities.

### How to Calculate Annual and Monthly Interest

All interest on mortgage loans is expressed as an annual interest amount, so if your mortgage interest rate is 8 percent, that’s the annual rate. But most mortgages are paid on a monthly basis, so you sometimes need to calculate how much interest you actually paid in one month based on that annual rate.

First, look at an annual interest problem:

You borrow \$200,000 at 5 percent for 30 years in an amortized mortgage loan. How much interest will you pay the first year?

Remember that in a mortgage loan, the interest rate is always quoted annually and is always based on the loan’s unpaid balance:

Loan amount × interest rate = first year’s interest

\$200,000 × 0.05 = \$10,000

The 30 years doesn’t matter. It’s extra information to confuse you.

Now here’s a monthly problem with different numbers:

You borrow \$300,000 at 4 percent interest for 30 years in an amortized loan. What is the first month’s interest on the loan?

Loan amount × interest rate = first year’s interest

\$300,000 × 0.04 = \$12,000 annual interest

You wind up with \$12,000 for the first year’s interest. To figure out the first month’s interest, all you have to do is divide the first year’s interest by 12:
First year’s interest / 12 months = first month’s interest

\$12,000 / 12 = \$1,000 first month’s interest

Note that this monthly interest calculation works this way only for the first month’s interest.

Test writers may go further and ask you to calculate the second month’s interest. To answer the question, you need to know what the total monthly payment is, and the test writers will tell you. I’ll continue using the numbers from the previous problem. In this case, the monthly payment, which includes principal and interest, is \$1,432 (rounded), information they have to give you. The question is how much is the second month’s interest payment:

\$1,432 (rounded) (monthly payment) – \$1,000 (first month’s interest) = \$432 (principal payment)

\$300,000 (loan amount) – \$432 (first month’s principal payment) = \$299,568 (loan balance after first month’s payment)

\$299,568 (loan balance after first payment) × 0.04 (annual interest rate) = \$11,982.72 (interest owed for the next 12 months)

\$11,982.72 (rounded) (interest owed for the next 12 months) / 12 months = \$998,56 (interest paid for the first month of that next 12-month period, which is, in fact, the second month of the loan term of the loan)

What you need to remember here is that in an amortized loan, you’re only reducing the amount you owe by the amount of principal you pay each month and not by the amount of the total payment, because each payment includes interest and principal.

### How to Calculate Total Interest

A type of interest problem that seems to confuse people is the calculation of total interest. Total interest is the amount of interest you pay during the entire life of the loan, assuming that you pay off the loan by making the payments within the required time frame. In general, banks provide these numbers to people, but you need to be familiar with this calculation because it is fair game on an exam.

Say you borrow \$300,000 at 5 percent for 30 years in an amortized mortgage loan. Your monthly payments are \$1,610 (rounded). What is the total interest on the loan?

Most people fool around with the 5 percent for a while, but you don’t need the percentage rate of the mortgage loan to work this problem. Watch this, because you’re not going to believe how easy it is:

\$1,610 (monthly payment) × 12 months × 30 years = \$579,600 total payments during the loan’s 30-year term

\$579,600 – \$300,000 (original loan amount) = \$279,600 interest paid during the course of the loan

Don’t forget that every amortized loan payment contains part principal and part interest. In this example in 30 years, you pay a total of \$579,600 in principal and interest. So if you subtract the principal, or the amount you borrowed, what you have left is interest. It’s also a good demonstration of why you may want to pay that mortgage off as soon as possible.

## How to Calculate Monthly Payments

Unless you use a financial calculator, you’re going to calculate mortgage payments using a mortgage table. These tables, which are arranged according to the percentage of interest and years of the mortgage term, provide the monthly payment to amortize, or pay off interest and principal, for a \$1,000 mortgage loan. After you get that monthly payoff number, which sometimes is called the payment factor, you multiply it by the number of thousands of dollars of the mortgage loan (which you get by dividing the loan amount by \$1,000).

The factor for a 20-year loan at 6 percent is \$7.16. What is the monthly payment for a \$150,000 loan?

\$150,000 / \$1,000 = 150 (units of a \$1,000)

150 × \$7.16 (factor to pay off \$1,000) = \$1,074 per month

If you run into a problem like this on the exam, you’ll either get a sample of a mortgage table or be given the payment factor you need to solve the problem. You’ll have to remember the formula in the example. In the real world, that is, when you have your license and are working on your first million, printed mortgage tables, many online mortgage calculation sites, and financial calculators can make all this relatively simple.