A buyer obtains a loan for $200,000 at 6% annual interest. What is the monthly interest payment for the first month?
Audio Lesson
Duration: 2:43
Question & Answer
Review the question and all answer choices
$1,200
The figure of $1,200 does not result from any correct application of 6% annual interest to a $200,000 loan — it might arise from incorrectly using a 7.2% annual rate or making an arithmetic error, and it overstates the actual monthly interest by $200.
$1,000
$12,000
The figure of $12,000 represents the correct ANNUAL interest on the loan ($200,000 × 6% = $12,000) but fails to convert it to a monthly figure by dividing by 12 — this is the most common calculation error on this type of question and represents forgetting the final step of the monthly conversion.
$600
The figure of $600 would result from applying a 3% rate (half of 6%) to the full loan amount, or from applying the correct 6% rate to half the loan amount — neither of which reflects the problem's parameters, and this answer may trap test-takers who confuse monthly rate (0.5%) with annual rate (6%) by incorrectly applying 0.5% directly to the annual balance rather than to the monthly balance.
Why is this correct?
The correct monthly interest for the first month is $1,000, calculated by multiplying the principal balance ($200,000) by the annual interest rate (6%) to get annual interest ($12,000), then dividing by 12 months to get the monthly interest ($1,000). This is the standard simple interest calculation used in virtually all residential mortgage products in the United States, and it represents the interest portion of the very first monthly payment before any principal has been repaid. The Truth in Lending Act (TILA, 15 U.S.C. § 1601) requires lenders to disclose this interest calculation methodology in the loan's Annual Percentage Rate (APR) disclosure.
Deep Analysis
AI-powered in-depth explanation of this concept
Mortgage interest calculations are fundamental to real estate finance because interest accrues on the outstanding principal balance, and in the early months of an amortizing loan, the vast majority of each payment is interest rather than principal reduction. The first month's interest is the purest interest calculation — there is no prior payment history, so the full principal balance of $200,000 is subject to the annual interest rate. Converting an annual rate to a monthly rate by dividing by 12 is essential because lenders charge interest monthly, not annually, and this conversion is the mathematical bridge between the loan terms stated in the note and the actual monthly payment obligation. This concept underpins the entire amortization schedule that governs how a 30-year mortgage gradually shifts from mostly interest to mostly principal payments over time.
Knowledge Background
Essential context and foundational knowledge
The standardization of monthly mortgage interest calculations in the United States was formalized through the development of the secondary mortgage market, particularly with the creation of Fannie Mae in 1938 and Freddie Mac in 1970, which required uniform loan documentation and calculation methods. Before standardization, mortgage terms varied widely, with some lenders using add-on interest methods that front-loaded interest costs in ways that were difficult for borrowers to understand. The Truth in Lending Act of 1968 and Regulation Z mandated clear disclosure of interest calculations, including the distinction between nominal interest rates and APR. Today, the Consumer Financial Protection Bureau (CFPB) oversees these disclosures through the Loan Estimate and Closing Disclosure forms introduced under the TRID rules in 2015.
Podcast Transcript
Full conversation between instructor and student
Instructor
Hey there, welcome back to our real estate license exam prep podcast. Today, we're diving into some real estate math. Are you ready to tackle this question with me?
Student
Absolutely, I'm ready. What's the question?
Instructor
Great! Here we go: A buyer obtains a loan for $200,000 at 6% annual interest. What is the monthly interest payment for the first month?
Student
Hmm, that's an interesting one. Do we need to do some division here?
Instructor
Exactly! This question is testing your ability to convert an annual interest rate to a monthly payment. It's a fundamental skill you'll use a lot in real estate.
Student
Got it. So, how do we do that?
Instructor
First, you calculate the annual interest amount by multiplying the loan amount by the annual interest rate. So, $200,000 times 0.06 equals $12,000.
Student
Okay, so the annual interest is $12,000. But how do we get the monthly interest?
Instructor
That's the tricky part. You need to divide the annual interest by 12 to get the monthly payment. So, $12,000 divided by 12 is $1,000.
Student
Oh, I see! So, the correct answer is B, $1,000?
Instructor
Yes, that's right! The correct answer is B because it properly converts the annual interest to a monthly amount.
Student
But why are the other options wrong?
Instructor
Let's go through them quickly. Option A is incorrect because it represents half of the annual interest divided by 6 months, which is not the correct calculation. Option C is wrong because it just shows the annual interest amount without dividing by 12. And option D is incorrect because it represents 1/4 of the annual interest divided by 3 months, which is another common mistake.
Student
Got it, I see the confusion now. It's easy to forget to divide by 12 or get the numbers mixed up.
Instructor
Absolutely. A memory technique can be helpful here. Think of the annual interest as a yearly pizza divided into 12 equal slices. Each slice represents one month's interest payment.
Student
That's a great way to visualize it! Thanks for that tip.
Instructor
You're welcome! And remember, for interest questions, always divide the annual interest by 12 to find the monthly payment. It's a quick way to eliminate wrong answers.
Student
Thanks for the tips, I'll keep that in mind. I feel more confident about this now.
Instructor
You should! And that wraps up our discussion on this question. Keep practicing, and you'll be ready to tackle any real estate math question that comes your way. Stay tuned for more episodes of our real estate license exam prep podcast. Good luck!
Use the 'Annual to Monthly Bridge': Annual Interest ÷ 12 = Monthly Interest, or think of it as 'yearly salary converted to monthly paycheck.' If you earn $12,000/year, you get $1,000/month — the same math applies to mortgage interest. Visualize the number 12 as a bridge connecting the annual figure ($12,000) to the monthly figure ($1,000), and never forget to cross that bridge when the question asks for a monthly amount.
When you see an annual interest rate question, visualize dividing the annual amount into 12 equal parts to find the monthly payment.
Whenever a real estate math question involves interest and asks for a monthly figure, your mandatory final step is always dividing by 12 — build this into a mental checklist. The exam routinely includes the correct annual interest as a wrong answer choice (in this case, $12,000) specifically to catch test-takers who stop one step early. Before selecting your answer, confirm the question asks for monthly or annual interest and verify your answer matches that time period.
Real World Application
How this concept applies in actual real estate practice
James closes on his first home purchase on March 1st, borrowing $200,000 at 6% annual interest with a 30-year fixed-rate mortgage. His first monthly payment is due April 1st. The lender calculates his first month's interest as $200,000 × 6% ÷ 12 = $1,000. His total monthly payment might be $1,199 (principal + interest for a standard amortizing loan), meaning only $199 goes toward reducing his principal balance in that first payment, while $1,000 goes to interest. Over time, as his principal decreases, the interest portion shrinks and the principal portion grows — a process clearly shown on his amortization schedule provided at closing.
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