Simple Interest for the New York Real Estate Exam

That compact method solves the arithmetic. The harder part is reading what the question actually asks, choosing the correct time unit and keeping simple-interest practice separate from mortgage amortization and annual percentage rate.

What is the simple-interest formula?

Use:

Interest = Principal × Rate × Time

Or:

I = P × R × T

Each letter has one job:

The Consumer Financial Protection Bureau uses this same formula in its calculating loan payments worksheet. The formula produces the interest amount, not the principal and not the total repayment amount.

If the question asks for principal plus simple interest, use a second step:

Total amount = Principal + Interest

Official source map

The New York State Department of State 77-hour curriculum lists interest under Subject 10, Real Estate Mathematics. The curriculum also identifies principal and interest as key terms and connects mathematics with real estate finance.

The Department of State salesperson page says the written examination is multiple choice, is based on the 77-hour curriculum and allows 1 1/2 hours after instructions. It does not publish an official number of interest questions or a subject-by-subject exam distribution.

The Consumer Financial Protection Bureau explains that principal is the amount borrowed and interest is the lender's charge. Its guidance also distinguishes a mortgage interest rate from annual percentage rate, or APR. These definitions support the vocabulary in this lesson. They do not mean a typical amortized mortgage can be solved with the simple-interest formula for its full term.

What does principal mean?

Principal is the starting amount on which a simple-interest problem tells you to calculate interest. In a basic loan example, it is the amount borrowed. In an investment example, it can be the amount deposited or invested.

Suppose a problem says:

A borrower receives a $240,000 loan at 6% simple interest for nine months.

The principal is $240,000. It is not the purchase price unless the problem says the loan equals the purchase price. It is not the down payment, total repayment or monthly payment.

In a real mortgage, the outstanding principal balance can decline as payments are applied. The CFPB explains how mortgage principal is paid down through amortization. A simple-interest exercise normally gives one principal amount and a defined period. Read the facts instead of importing a mortgage schedule into a one-step problem.

How do you convert the interest rate?

The rate in I = P × R × T is an annual decimal rate unless the question clearly provides another convention.

To change a percentage to a decimal, divide by 100. A rate of 6% becomes 0.06, not 6. A rate of 0.75% becomes 0.0075, not 0.75.

Use a reasonableness check. Six percent of $100,000 for one full year is $6,000. If a calculator produces $600,000, the percentage was entered as a whole number rather than a decimal.

For a deeper review of percentage roles and decimal conversions, use Part, Rate and Whole for New York Real Estate Math.

How do you express time in years?

Because the rate is annual, time must be stated in years or as a fraction of a year.

Whole years

Use the number directly:

• 1 year = 1
• 2 years = 2
• 2.5 years = 2.5

Months

Divide the number of months by 12:

• 3 months = 3 ÷ 12 = 0.25 year
• 6 months = 6 ÷ 12 = 0.50 year
• 8 months = 8 ÷ 12 = 2/3 year
• 9 months = 9 ÷ 12 = 0.75 year
• 15 months = 15 ÷ 12 = 1.25 years

Days

Use the denominator stated in the problem:

Time = Number of days ÷ Days in the stated year

If the problem directs you to use a 360-day year, 90 days is 90 ÷ 360 = 0.25 year.

If it directs you to use a 365-day year, 90 days is 90 ÷ 365, approximately 0.246575 year.

The two conventions produce different answers. Do not choose 360 or 365 from habit. Use the convention printed in the question. If no convention is supplied in an educational problem, the item is incomplete unless its context establishes one.

How do you calculate simple interest?

Example 1: One full year

A borrower receives $180,000 at 5% simple interest for one year. How much interest accrues?

I = $180,000 × 0.05 × 1

I = $9,000

The interest is $9,000. If the question asked for principal plus interest, the total would be:

$180,000 + $9,000 = $189,000

Example 2: Several years

A $75,000 principal amount earns 4.8% simple interest for three years.

I = $75,000 × 0.048 × 3

I = $10,800

The total amount after three years is:

$75,000 + $10,800 = $85,800

Simple interest is calculated on the stated principal in this example. It does not add the first year's interest to principal before calculating the second year's interest.

Example 3: Months

A $320,000 principal amount carries 6% simple interest for nine months.

First convert time:

T = 9 ÷ 12 = 0.75 year

Then calculate:

I = $320,000 × 0.06 × 0.75

I = $14,400

The interest for nine months is $14,400.

Example 4: Days using a 360-day year

A problem directs you to calculate simple interest on $250,000 at 7.2% for 45 days using a 360-day year.

T = 45 ÷ 360 = 0.125 year

I = $250,000 × 0.072 × 0.125

I = $2,250

Example 5: Days using a 365-day year

Use the same principal, rate and 45-day period, but follow a stated 365-day year.

T = 45 ÷ 365

I = $250,000 × 0.072 × (45 ÷ 365)

I = $2,219.18, rounded to the nearest cent

The difference comes entirely from the day-count convention. It is not a rounding mistake.

How do you solve for principal?

When interest, rate and time are known, divide:

P = I ÷ (R × T)

Example 6: Find the original principal

A loan produces $8,400 in simple interest at 7% for eight months. What is the principal?

Convert time:

T = 8 ÷ 12 = 2/3 year

Rearrange and solve:

P = $8,400 ÷ (0.07 × 2/3)

P = $180,000

Check the result:

$180,000 × 0.07 × 2/3 = $8,400

Use parentheses around R × T. Dividing by the rate and then multiplying by time would change the relationship.

How do you solve for the rate?

When interest, principal and time are known:

R = I ÷ (P × T)

The calculator returns a decimal. Multiply by 100 to state the answer as a percentage.

Example 7: Find the annual rate

A $400,000 principal amount produces $15,000 in simple interest over nine months.

T = 9 ÷ 12 = 0.75 year

R = $15,000 ÷ ($400,000 × 0.75)

R = 0.05 = 5%

The annual simple-interest rate is 5%.

Do not report 0.05%. The decimal 0.05 equals 5% after conversion.

How do you solve for time?

When interest, principal and rate are known:

T = I ÷ (P × R)

The answer is in years when the rate is annual. Convert to months only if the question asks for months.

Example 8: Find the number of months

How long will it take $150,000 to produce $5,625 in simple interest at 6% annually?

T = $5,625 ÷ ($150,000 × 0.06)

T = 0.625 year

Convert years to months:

0.625 × 12 = 7.5 months

The time is 7.5 months.

How can you identify the missing variable quickly?

Translate the wording before touching the calculator.

Write I = P × R × T, circle the requested quantity and label every supplied number. This takes a few seconds and prevents a rate, month count or total amount from being placed in the wrong role.

The New York real estate math formula map shows how this method fits with the other math relationships in the curriculum.

Is simple interest the same as compound interest?

No. In the basic simple-interest model, interest is calculated on the stated principal for the stated time. Compound interest can calculate later interest on principal plus previously added interest.

Consider $10,000 at 5% for two years:

Simple interest:

$10,000 × 0.05 × 2 = $1,000

The simple-interest total is $11,000.

If a separate problem expressly required annual compounding, its method would be different because the second year's calculation could use a larger balance. Do not introduce compounding when a question says simple interest. Avoid using the simple-interest formula when a question expressly provides a compounding rule.

Is simple interest the same as mortgage amortization?

No. The CFPB explains that with a typical fixed-rate mortgage, the combined scheduled principal-and-interest payment may remain level while the portions applied to principal and interest change over time. Early in the term, more of that payment goes to interest because the outstanding balance is higher. That process is amortization.

The CFPB also explains that mortgage lenders use a standard payment formula based on the loan amount, term and interest rate. A full amortized-payment calculation is not the same as multiplying the original principal by rate and the full term.

Use I = P × R × T when the educational question asks for simple interest or supplies facts that clearly establish that relationship. Use an amortization method only when the question gives the necessary mortgage-payment framework.

Is the interest rate the same as APR?

No. The CFPB defines a mortgage interest rate as the yearly cost of borrowing expressed as a percentage rate, without fees and other charges. APR is a broader measure that can include the interest rate, points, mortgage broker fees and certain other charges.

That distinction matters in both vocabulary and math:

• a stated interest rate can be the R in a simple-interest problem
• APR is not automatically the R in that formula
• points and other loan charges require their own calculation when supplied
• comparing real loans requires more than a one-step simple-interest result

The next article in this math sequence covers discount points and loan charges separately.

Is interest the same as the total mortgage payment?

No. Interest is one component. The CFPB's PITI explanation identifies principal, interest, taxes and insurance as four basic elements commonly associated with a monthly mortgage payment. Mortgage insurance or other amounts may also apply.

If a question asks only for simple interest, return the interest amount. If it asks for principal plus interest, add those two figures. If it asks for a total mortgage payment, use every component and instruction the problem supplies rather than treating interest as the full payment.

What are the most common simple-interest mistakes?

Entering 6 instead of 0.06

A percentage must be converted to a decimal before it is used as R in ordinary multiplication.

Treating months as years

Nine months is 9 ÷ 12, or 0.75 year. Entering 9 as time would calculate nine years.

Mixing a monthly rate with annual time

Keep the rate and time units consistent. This lesson uses an annual rate and time expressed in years.

Guessing the day-count convention

A 360-day result and a 365-day result differ. Follow the convention stated in the problem.

Returning total repayment when the question asks for interest

P × R × T produces interest. Add principal only when the requested quantity includes it.

Using purchase price as principal

Principal is the amount the problem says is subject to interest. A property's price and loan principal can be different.

Confusing APR with the note rate

APR can reflect charges beyond interest. Read the term given instead of treating the labels as interchangeable.

Applying simple interest to a full amortized mortgage

A typical amortized mortgage changes the principal balance over time. The one-step simple-interest formula does not reproduce its complete payment schedule.

What is a reliable exam-day workflow?

Use this six-step process:

1. Write I = P × R × T.
2. Identify what the question asks you to find.
3. Label principal, rate and time from the facts.
4. Convert the percentage to a decimal and time to years.
5. Solve, then convert the final unit if needed.
6. Estimate and substitute the answer back into the formula.

Example check: if $200,000 is borrowed at 6% for half a year, one full year's interest would be $12,000. Half a year's interest should be $6,000. An answer of $60,000 or $600 suggests a conversion error.

Review the complete Real Estate Mathematics study guide when you need to connect interest with percentages, commissions, points, taxes, area and prorations.

Can you solve these original practice questions?

Practice 1

A $275,000 principal amount carries 4.8% simple interest for 15 months. What is the interest?

A. $13,200
B. $16,500
C. $19,800
D. $33,000

Answer: B. Fifteen months is 15 ÷ 12 = 1.25 years. Interest is $275,000 × 0.048 × 1.25 = $16,500.

Practice 2

A borrower pays $6,750 in simple interest on $180,000 for nine months. What annual rate was used?

A. 3%
B. 4%
C. 5%
D. 6%

Answer: C. Time is 0.75 year. R = $6,750 ÷ ($180,000 × 0.75) = 0.05, or 5%.

Practice 3

A problem directs you to use a 360-day year. What is the simple interest on $360,000 at 5% for 72 days?

A. $2,500
B. $3,600
C. $4,500
D. $18,000

Answer: B. Time is 72 ÷ 360 = 0.20 year. Interest is $360,000 × 0.05 × 0.20 = $3,600.

Practice 4

$9,000 of simple interest accrues at 6% for ten months. What principal produced it?

A. $150,000
B. $162,000
C. $180,000
D. $216,000

Answer: C. Time is 10 ÷ 12, or 5/6 year. P = $9,000 ÷ (0.06 × 5/6) = $180,000.

Practice 5

A $96,000 principal amount earns $8,640 in simple interest at 4.5% annually. How long was the money used?

A. 18 months
B. 20 months
C. 24 months
D. 27 months

Answer: C. T = $8,640 ÷ ($96,000 × 0.045) = 2 years. Two years equals 24 months.

Practice 6

A question asks for the total amount due on $125,000 after one year at 8% simple interest. What is the answer?

A. $10,000
B. $125,000
C. $133,000
D. $135,000

Answer: D. Interest is $125,000 × 0.08 × 1 = $10,000. Total due is $125,000 + $10,000 = $135,000.

Practice 7

Which statement is accurate?

A. APR and the mortgage interest rate are interchangeable.
B. The simple-interest formula calculates a complete amortization schedule.
C. Principal is the amount on which the stated simple interest is calculated.
D. Nine months should be entered as 9 when the rate is annual.

Answer: C. The other choices confuse APR with interest rate, simple interest with amortization, or months with years.

Frequently asked questions

What formula should I memorize for simple interest?

Memorize I = P × R × T: interest equals principal times the annual decimal rate times time in years.

How do I convert months for simple interest?

Divide the number of months by 12. For example, nine months is 0.75 year and 15 months is 1.25 years.

Should I use 360 or 365 days?

Use the year length stated in the question. The two conventions produce different results, so an educational item should provide or establish the required convention.

Does the formula give interest or the total amount owed?

P × R × T gives the simple-interest amount. Add principal only if the question asks for principal plus interest or total amount due.

Is principal the property price?

Not necessarily. Principal is the amount subject to interest. A purchase price, loan amount and down payment can be three different figures.

Is simple interest used to calculate a typical mortgage payment?

Not by itself. Typical mortgage payments use an amortization formula in which the outstanding balance and allocation between principal and interest change over time.

Is an interest rate the same as APR?

No. An interest rate is the cost of borrowing expressed as a rate. APR is a broader measure that can include the interest rate and specified loan charges.

How many simple-interest questions are on the New York exam?

The Department of State curriculum includes interest in Real Estate Mathematics, but the Department does not publish an official count of simple-interest questions or a subject-by-subject weighting.

Sources and verification notes

This article was checked against official sources available on August 27, 2026. It teaches original exam-preparation examples and does not reproduce state examination questions.

• New York State Department of State, Real Estate Salesperson 77-Hour Curriculum
• New York State Department of State, Real Estate Salesperson
• Consumer Financial Protection Bureau, Calculating loan payments worksheet
• Consumer Financial Protection Bureau, Principal and interest payment versus total monthly payment
• Consumer Financial Protection Bureau, Mortgage interest rate versus APR
• Consumer Financial Protection Bureau, How paying down a mortgage works
• Consumer Financial Protection Bureau, How mortgage lenders calculate monthly payments
• Consumer Financial Protection Bureau, PITI

Use this lesson for education and exam preparation. For an actual loan, rely on the promissory note, required disclosures and guidance from qualified lending, legal or tax professionals as appropriate.