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Percentages: commissions, interest, appreciation and depreciation, and points
Finish →Question 1 of 40
Which decimal represents 2.5% for a commission calculation?
Reveal answer
Correct answer: 0.025
Percent means per hundred: 2.5 ÷ 100 = 0.025. Multiply the commission base by 0.025.
Question 2 of 40
A property sells for $360,000. The agreed total commission is 5% of the sale price. What is the total commission before any splits?
Reveal answer
Correct answer: $18,000
Convert 5% to 0.05: 5 ÷ 100 = 0.05. Multiply $360,000 × 0.05 = $18,000. No split is requested.
Question 3 of 40
A $500,000 sale produces a 4% total commission. The listing brokerage receives 60% of the commission, and its salesperson receives 70% of that brokerage share. What does the salesperson receive?
Reveal answer
Correct answer: $8,400
4 ÷ 100 = 0.04; $500,000 × 0.04 = $20,000 total commission. 60 ÷ 100 = 0.60; $20,000 × 0.60 = $12,000 brokerage share. 70 ÷ 100 = 0.70; $12,000 × 0.70 = $8,400 salesperson share.
Question 4 of 40
A $24,000 total commission equals 6% of the sale price. What was the sale price?
Reveal answer
Correct answer: $400,000
6 ÷ 100 = 0.06. Base = part ÷ decimal rate, so $24,000 ÷ 0.06 = $400,000. Check: $400,000 × 0.06 = $24,000.
Question 5 of 40
Which expression calculates simple interest when the rate is annual and principal remains unchanged?
Reveal answer
Correct answer: Principal × annual decimal rate × time in years
Simple interest equals principal multiplied by the annual decimal rate and the elapsed time in years. Months must first be divided by 12.
Question 6 of 40
An unchanged $80,000 loan balance accrues simple interest at 9% annually for four months. How much interest accrues?
Reveal answer
Correct answer: $2,400
9 ÷ 100 = 0.09. Annual interest = $80,000 × 0.09 = $7,200. Time = 4 ÷ 12 = 1/3 year. Interest = $7,200 × 1/3 = $2,400.
Question 7 of 40
A $250,000 property appreciates by 8%. What is its value after the increase?
Reveal answer
Correct answer: $270,000
8 ÷ 100 = 0.08. Increase = $250,000 × 0.08 = $20,000. New value = $250,000 + $20,000 = $270,000.
Question 8 of 40
A property increases 20% in value and then decreases 20% from its new value. Which statement best explains the result?
Reveal answer
Correct answer: It ends below its starting value because the decrease uses a larger base.
The factors are 1 + 0.20 = 1.20 and 1 − 0.20 = 0.80. Their product is 1.20 × 0.80 = 0.96, leaving 96% of the original value, a 4% loss. The decline applies to the higher intermediate value.
Question 9 of 40
For mortgage pricing, one point equals which amount?
Reveal answer
Correct answer: 1% of the loan amount
One point is 1% of the loan amount. Purchase price, down payment, and monthly interest are different bases or measures.
Question 10 of 40
A buyer pays $400,000 for a home and borrows $320,000. The loan carries 1.5 points. What is the charge for points?
Reveal answer
Correct answer: $4,800
1.5 points = 1.5%; 1.5 ÷ 100 = 0.015. Points cost = $320,000 × 0.015 = $4,800. The $400,000 purchase price is not the base.
Question 11 of 40
A borrower pays $5,625 in points on a $225,000 loan. How many points were charged?
Reveal answer
Correct answer: 2.5 points
Rate = $5,625 ÷ $225,000 = 0.025. Convert to percent: 0.025 × 100 = 2.5%. Since one point equals 1%, the charge is 2.5 points.
Question 12 of 40
A salesperson multiplies a brokerage's commission share by the salesperson's split percentage. What is the base in that calculation?
Reveal answer
Correct answer: The brokerage's commission share
The base is the amount to which the percentage applies. For this split it is the brokerage's commission share; the salesperson's compensation is the resulting part.
Question 13 of 40
A property is worth $288,000 after a 10% decline. What was its value immediately before that decline?
Reveal answer
Correct answer: $320,000
10 ÷ 100 = 0.10. The remaining-value factor is 1 − 0.10 = 0.90. Original value = $288,000 ÷ 0.90 = $320,000. Check: $320,000 × 0.10 = $32,000; $320,000 − $32,000 = $288,000.
Question 14 of 40
A $300,000 property appreciates 5% during each of two successive years. What is its value at the end of the second year?
Reveal answer
Correct answer: $330,750
5 ÷ 100 = 0.05. Year one gain = $300,000 × 0.05 = $15,000; year one value = $315,000. Year two gain = $315,000 × 0.05 = $15,750; final value = $315,000 + $15,750 = $330,750.
Question 15 of 40
A loan has a 6% contract interest rate and a 6.4% annual percentage rate. Which rate should be used to calculate one month of simple interest on its unchanged principal?
Reveal answer
Correct answer: 6%, the contract interest rate
Use the 6% contract interest rate for simple interest. The annual percentage rate is a borrowing-cost disclosure measure, not an additional or substitute accrual rate for this calculation.
Question 16 of 40
For a covered New York consumer mortgage transaction, federal Truth in Lending law requires the finance charge to be expressed using which percentage term?
Reveal answer
Correct answer: Annual percentage rate
15 U.S.C. § 1638(a)(4) requires the finance charge to be expressed as an annual percentage rate for covered transactions. This is federal law applying in New York.
Question 17 of 40
A $480,000 sale produces $21,600 in total commission. What commission rate was applied to the sale price?
Reveal answer
Correct answer: 4.5%
Divide part by base: $21,600 ÷ $480,000 = 0.045. Convert to percent: 0.045 × 100 = 4.5%. Check: $480,000 × 0.045 = $21,600.
Question 18 of 40
A brokerage receives $15,000 in commission and pays its salesperson 65% of that amount. How much does the brokerage retain?
Reveal answer
Correct answer: $5,250
Retained percentage = 100% − 65% = 35%. Convert: 35 ÷ 100 = 0.35. Retained amount = $15,000 × 0.35 = $5,250. The salesperson receives $15,000 × 0.65 = $9,750.
Question 19 of 40
A loan's unchanged principal is $150,000. It accrues $4,500 in simple interest over six months. What is its annual interest rate?
Reveal answer
Correct answer: 6%
Time = 6 ÷ 12 = 0.5 year. Annual decimal rate = $4,500 ÷ ($150,000 × 0.5) = $4,500 ÷ $75,000 = 0.06. Convert: 0.06 × 100 = 6%.
Question 20 of 40
Which amount is the base when calculating a property's percentage appreciation over a specified period?
Reveal answer
Correct answer: The property value at the beginning of the period
Percentage appreciation compares the increase with the starting value. The increase is the part, and the beginning value is the base.
Question 21 of 40
A property's value rises from $240,000 to $270,000. What is the percentage appreciation over that period?
Reveal answer
Correct answer: 12.5%
Increase = $270,000 − $240,000 = $30,000. Rate = $30,000 ÷ $240,000 = 0.125. Percent appreciation = 0.125 × 100 = 12.5%.
Question 22 of 40
A buyer borrows $280,000 to buy a $350,000 home and pays two points. A worksheet shows $7,000 in points. What correction is needed?
Reveal answer
Correct answer: Use $5,600, based on the loan amount.
Two points = 2 ÷ 100 = 0.02 of the loan. $280,000 × 0.02 = $5,600. The erroneous $7,000 equals $350,000 × 0.02 and uses the purchase price.
Question 23 of 40
A borrower says, 'Paying one discount point means my interest rate will fall by one percentage point.' What is the best response?
Reveal answer
Correct answer: One point measures a charge of 1% of the loan; the rate reduction depends on the offered terms.
A discount point is an upfront interest charge equal to 1% of the loan amount. Its definition specifies its cost, not a fixed reduction in the interest rate.
Question 24 of 40
A property worth $500,000 declines 6% in market value. What is the dollar amount of the decline?
Reveal answer
Correct answer: $30,000
6 ÷ 100 = 0.06. Dollar decline = $500,000 × 0.06 = $30,000. The remaining value would be $500,000 − $30,000 = $470,000, but the question asks for the decline.
Question 25 of 40
A seller wants $380,000 after paying a commission equal to 5% of the sale price. Ignore all other expenses and debts. What sale price is required?
Reveal answer
Correct answer: $400,000
The seller retains 100% − 5% = 95%, or 0.95, of price. Price = $380,000 ÷ 0.95 = $400,000. Check: $400,000 × 0.05 = $20,000 commission; $400,000 − $20,000 = $380,000.
Question 26 of 40
A salesperson receives 75% of the sponsoring brokerage's commission share. The salesperson received $9,000. What was the brokerage's share before paying the salesperson?
Reveal answer
Correct answer: $12,000
75 ÷ 100 = 0.75. Brokerage share = $9,000 ÷ 0.75 = $12,000. Check: $12,000 × 0.75 = $9,000.
Question 27 of 40
Which description correctly distinguishes a simple-interest calculation from an amortizing mortgage payment calculation?
Reveal answer
Correct answer: Simple interest calculates interest for a stated principal, rate, and time; it does not by itself calculate the full amortizing payment.
Principal × annual decimal rate × time gives interest. A full amortizing payment also repays principal; this simple-interest formula alone does not determine that payment.
Question 28 of 40
An unchanged loan balance accrues simple interest at 8% annually. After 18 months, the interest totals $12,000. What is the principal?
Reveal answer
Correct answer: $100,000
8 ÷ 100 = 0.08. Time = 18 ÷ 12 = 1.5 years. Rate × time = 0.08 × 1.5 = 0.12. Principal = $12,000 ÷ 0.12 = $100,000.
Question 29 of 40
A $400,000 property declines 10% in the first year and 5% in the second year. What is its value after both declines?
Reveal answer
Correct answer: $342,000
10% = 0.10 and 5% = 0.05. First loss = $400,000 × 0.10 = $40,000; remaining value = $360,000. Second loss = $360,000 × 0.05 = $18,000; final value = $360,000 − $18,000 = $342,000.
Question 30 of 40
A property is worth $250,000 after appreciating 25%. What was its value before the appreciation?
Reveal answer
Correct answer: $200,000
25 ÷ 100 = 0.25. Growth factor = 1 + 0.25 = 1.25. Original value = $250,000 ÷ 1.25 = $200,000. Check: $200,000 × 0.25 = $50,000; $200,000 + $50,000 = $250,000.
Question 31 of 40
A buyer finances 80% of a $450,000 purchase price. The loan carries 1.25 points. What is the charge for points?
Reveal answer
Correct answer: $4,500
80 ÷ 100 = 0.80; loan = $450,000 × 0.80 = $360,000. 1.25 points = 1.25 ÷ 100 = 0.0125. Charge = $360,000 × 0.0125 = $4,500.
Question 32 of 40
When finding a percentage rate from a dollar part and a dollar base, which procedure is correct?
Reveal answer
Correct answer: Divide the part by the base, then multiply by 100.
Part ÷ base gives the decimal rate. Multiplying that decimal by 100 expresses the rate as a percent.
Question 33 of 40
On a $300,000 loan, Offer One charges two points and Offer Two charges 0.75 point. Considering only points, how much less does Offer Two charge?
Reveal answer
Correct answer: $3,750
Two points = 0.02; Offer One costs $300,000 × 0.02 = $6,000. 0.75 point = 0.0075; Offer Two costs $300,000 × 0.0075 = $2,250. Difference = $6,000 − $2,250 = $3,750.
Question 34 of 40
A buyer reduces a planned loan from $300,000 to $260,000. Both amounts would carry two points. How does the reduction affect the points charge?
Reveal answer
Correct answer: It decreases by $800.
Two points = 2 ÷ 100 = 0.02. Original charge = $300,000 × 0.02 = $6,000. Revised charge = $260,000 × 0.02 = $5,200. Reduction = $6,000 − $5,200 = $800.
Question 35 of 40
A property falls in value from $200,000 to $160,000. What percentage increase from $160,000 would restore its original value?
Reveal answer
Correct answer: 25%
Required gain = $200,000 − $160,000 = $40,000. Use the current base: $40,000 ÷ $160,000 = 0.25. Convert: 0.25 × 100 = 25%. Check: $160,000 × 1.25 = $200,000.
Question 36 of 40
At a fixed annual simple-interest rate, with no principal changes, how does interest for nine months compare with interest for three months on the same loan?
Reveal answer
Correct answer: It is three times as much.
Three months = 3/12 = 0.25 year; nine months = 9/12 = 0.75 year. With principal and rate fixed, the interest ratio is 0.75 ÷ 0.25 = 3. Nine months produces three times the interest.
Question 37 of 40
Two unchanged loan balances of $100,000 accrue simple interest for one year. One has a 6% annual rate and the other a 6.5% annual rate. How much more interest does the second loan accrue?
Reveal answer
Correct answer: $500
6% = 0.06; first interest = $100,000 × 0.06 × 1 = $6,000. 6.5% = 0.065; second interest = $100,000 × 0.065 × 1 = $6,500. Difference = $6,500 − $6,000 = $500.
Question 38 of 40
Which statement describes appreciation rather than depreciation in a property's market value?
Reveal answer
Correct answer: The property's value increases relative to its earlier value.
Appreciation is an increase in property value. Depreciation is a decrease. Debt reduction may increase equity without any appreciation.
Question 39 of 40
A $600,000 sale has a 5% total commission. A brokerage receives 40% of that commission, and its salesperson receives 50% of the brokerage share. A worksheet pays the salesperson $15,000. What went wrong?
Reveal answer
Correct answer: The worksheet skipped the brokerage allocation; the correct payment is $6,000.
5% = 0.05; total commission = $600,000 × 0.05 = $30,000. Brokerage share = $30,000 × 0.40 = $12,000. Salesperson share = $12,000 × 0.50 = $6,000. The erroneous $15,000 equals $30,000 × 0.50 and omits the 40% allocation.
Question 40 of 40
A $200,000 loan carries one discount point paid separately upfront and accrues 6% simple interest on unchanged principal for six months. Considering only the point and that interest, what is the combined cost?
Reveal answer
Correct answer: $8,000
One point = 0.01; point cost = $200,000 × 0.01 = $2,000. Interest rate = 0.06; time = 6 ÷ 12 = 0.5 year. Interest = $200,000 × 0.06 × 0.5 = $6,000. Combined cost = $2,000 + $6,000 = $8,000.
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