Practice calculations: commission and GST, loan-to-value and debt service, mortgage interest and priority, property taxes, closing adjustments, condominium contributions, RMS areas and rates of return. References: the Real Estate Act and Rules, the Land Titles Act (LTA), the Municipal Government Act (MGA), the Condominium Property Act (CPA) and Regulation, the Residential Tenancies Act (RTA), RECA's Guide to the RMS and RECA's FRE and PRRE blueprints. Rates in examples are fictional. These are study notes for practice questions, not RECA material.
1. A seller's written service agreement sets the commission at 7% on the first $100,000 of the sale price and 3% on the balance. The home sells for $485,000. What is the commission before GST?
7% x $100,000 = $7,000; 3% x ($485,000 - $100,000) = 3% x $385,000 = $11,550; total $18,550. The 3% applies only to the balance above the first $100,000, not to the whole price. Commission terms are whatever the written service agreement states (Real Estate Act Rules, Rule 43; PRRE blueprint 5.1.2.4).
2. A home sells for $410,000. The seller pays a commission of 4% of the sale price, and GST at 5% is charged on the commission. What does the seller pay the brokerage in total?
Commission 4% x $410,000 = $16,400; GST 5% x $16,400 = $820; total $17,220. GST is charged on the commission, not on the sale price, and the 4% in the stem is a pre-GST rate (PRRE blueprint glossary, 'Real Estate Taxation Methodologies', which lists GST among transaction tax calculations).
3. Prairie Gate Realty's listing agreement pays 6% on the first $100,000 and 2.5% on the balance. It offers the buyer's brokerage 3.25% on the first $100,000 and 1.25% on the balance. The home sells for $640,000. What does the buyer's brokerage receive before GST?
Buyer's brokerage: 3.25% x $100,000 = $3,250 plus 1.25% x $540,000 = $6,750, total $10,000. The listing brokerage earns $19,500 in all and keeps $9,500. Applying 1.25% to the whole price gives $8,000. A brokerage may pay part of its commission to another licensed brokerage (Real Estate Act Rules, Rule 50(c)(ii)); under s.23 of the Real Estate Act, only the listing brokerage, which holds the service agreement with the seller, may sue the seller for the shared commission.
4. Kiran's brokerage receives $14,800 of commission (before GST) on her sale. Her agreement with the brokerage gives her 75% of that commission after the brokerage first deducts a $450 transaction fee. How much is Kiran paid?
Deduct the fee first: $14,800 - $450 = $14,350; 75% x $14,350 = $10,762.50. Taking 75% before deducting the fee gives $10,650. The brokerage pays commission to the associates registered with it (Real Estate Act Rules, Rule 50(c)(i)).
5. A brokerage was paid a commission of $24,150 before GST, calculated at a flat 3.5% of the sale price. What was the sale price?
Sale price = commission / rate = $24,150 / 0.035 = $690,000. Dividing by 0.35 or by 3.5 misplaces the decimal ($69,000, $6,900); adding 5% treats GST as part of the price ($724,500).
6. A seller wants to receive $400,000 after paying a commission of 4% of the sale price plus 5% GST on that commission. Ignoring all other costs, what is the lowest sale price that achieves this?
Commission with GST = 4% x 1.05 = 4.2% of the price, so the seller keeps 95.8%. Price = $400,000 / 0.958 = $417,536.53. Check: $417,536.53 x 4.2% = $17,536.53; $417,536.53 - $17,536.53 = $400,000. Adding 4.2% to $400,000 ($416,800) falls short because the commission is charged on the higher price.
7. A seller tells associate Marco: 'List my home at $380,000. Anything above that price is yours as commission.' Under s.24 of the Real Estate Act, how should Marco treat this offer?
Section 24(1) of the Real Estate Act prohibits a real estate broker from requesting or entering into an arrangement for a commission based on the difference between the listing price and the actual sale price, and from retaining a commission computed that way. A written agreement, a cap or disclosure does not cure it.
8. A commission is 7% on the first $100,000 and 3% on the balance. On a $750,000 sale, what is the commission as a single percentage of the price (before GST)?
7% x $100,000 = $7,000; 3% x $650,000 = $19,500; total $26,500. $26,500 / $750,000 = 3.53%. Averaging 7% and 3% (5.00%) ignores how much of the price falls in each tier; charging 3% on the full price on top of the $7,000 gives $29,500, or 3.93%; 3.00% ignores the higher first tier.
9. A brokerage's commission invoice shows a total of $21,500, which includes GST at 5%. What is the commission before GST?
A GST-inclusive amount equals 105% of the commission: $21,500 / 1.05 = $20,476.19 (GST $1,023.81). Taking 5% off the total ($20,425) uses the wrong base.
10. A $25,200 commission (before GST) is shared equally by the two brokerages. The buyer's brokerage pays a referral fee of 25% of its own share to a licensed Ontario brokerage that referred the buyer. How much is the referral fee?
The buyer's brokerage's share is $25,200 / 2 = $12,600; 25% x $12,600 = $3,150. Rule 50(c)(ii) of the Real Estate Act Rules allows a brokerage to pay part of its commission to a brokerage licensed under similar legislation outside Alberta.
11. Your seller has two offers. Offer A is $512,000 with an $8,000 credit to the buyer at closing; Offer B is $505,000 with no credit. Commission is 3.5% of the sale price plus 5% GST. Which offer leaves the seller more, and by how much?
Offer A: $512,000 - $8,000 - (3.675% x $512,000 = $18,816) = $485,184. Offer B: $505,000 - $18,558.75 = $486,441.25. B leaves $1,257.25 more. Ignoring the credit wrongly favours A; ignoring GST gives $1,245.00.
12. A buyer's brokerage is entitled to a $9,300 share of the commission, and GST at 5% must be added to it. How much GST applies to that share?
GST = 5% x $9,300 = $465. Backing GST out of $9,300 ($442.86) would only be right if the $9,300 already included GST.
13. Theo keeps 80% of each commission his brokerage receives, and the brokerage keeps 20% until it has collected $18,000 from him in the year; after that Theo keeps 100%. Before this deal the brokerage had collected $15,600 from him. This deal brings in $16,000 of commission. How much does Theo receive?
Room left under the cap: $18,000 - $15,600 = $2,400. The brokerage's 20% would be $3,200, but it may take only $2,400, so Theo receives $16,000 - $2,400 = $13,600. The brokerage pays commission to its own associates under Rule 50(c)(i).
14. A total commission of $19,860 before GST is split equally between the listing and the buyer's brokerages. With GST at 5% added, how much does each brokerage invoice?
Each share: $19,860 / 2 = $9,930; with 5% GST: $9,930 x 1.05 = $10,426.50.
15. A lender approves a $391,000 mortgage on a home valued at $460,000. What is the loan-to-value (LTV) ratio?
LTV = loan / value = $391,000 / $460,000 = 85.0%. The buyer's equity is the other 15.0%. LTV is a key affordability and risk measure in mortgage lending (FRE blueprint 2.2.2.10).
16. A buyer agrees to pay $610,000, but the appraisal comes in at $590,000. The lender lends up to 80% of the lower of price and appraised value. What is the smallest down payment the buyer needs?
Maximum loan = 80% x $590,000 = $472,000. Down payment = $610,000 - $472,000 = $138,000: 20% of the appraised value plus the $20,000 appraisal gap. Financing condition due diligence includes checking how the lender values the property (FRE blueprint 2.2.2.5).
17. In this scenario, the lender's policy requires a minimum down payment of 5% on the first $500,000 of the price and 10% on the portion above $500,000. What is the minimum down payment on a $640,000 home?
5% x $500,000 = $25,000; 10% x $140,000 = $14,000; total $39,000. Reversing the tiers gives $57,000. (The tiers are the lender policy given in the question, not a statement of current rules; affordability guidelines and down payments are part of 'Types of Mortgages, Impact' in the PRRE blueprint glossary.)
18. A buyer pays $450,000 with 5% down. In this scenario, a mortgage default insurance premium of 4.00% of the loan amount is added to the mortgage. What is the total mortgage after the premium is added?
Loan = $450,000 - 5% ($22,500) = $427,500. Premium = 4.00% x $427,500 = $17,100. Total = $444,600. The premium is based on the loan, not the price (premium rate given in the question, not a statement of current insurer rates).
19. A home worth $450,000 has a first mortgage of $300,000 and a second mortgage of $60,000. What is the combined loan-to-value ratio?
Combined LTV = all mortgage debt / value = ($300,000 + $60,000) / $450,000 = 80.0%. Using the first mortgage alone gives 66.7%.
20. An owner's home is worth $520,000 and the mortgage balance is $310,000. What is the owner's equity as a percentage of the home's value?
Equity = $520,000 - $310,000 = $210,000; $210,000 / $520,000 = 40.4%. 59.6% is the loan-to-value ratio, not the equity.
21. A buyer has $45,000 available for a down payment, and the lender will lend up to 90% of the purchase price. Ignoring legal fees and other costs, what is the highest price the buyer can pay?
The $45,000 must cover the 10% the lender will not lend: price = $45,000 / 0.10 = $450,000 (loan $405,000). $405,000 is the loan, not the price.
22. A buyer's gross income is $9,000 a month. In this scenario the lender limits housing costs (principal, interest, property taxes and heating) to 32% of gross income. Taxes will be $350 and heating $120 a month. What is the most the buyer can pay in principal and interest?
Housing limit = 32% x $9,000 = $2,880. Subtract taxes and heating: $2,880 - $350 - $120 = $2,410 for principal and interest. Debt-service ratios are key mortgage affordability determinants (FRE blueprint 2.2.2.10); the 32% limit is fictional, set in the question.
23. A borrower's housing costs (principal, interest, taxes and heating) are $2,650 a month, other debt payments are $900 a month, and gross income is $10,000 a month. What is the total debt service (TDS) ratio?
TDS = (housing costs + other debts) / gross income = ($2,650 + $900) / $10,000 = 35.5%. Housing costs alone give the gross debt service ratio (26.5%).
24. Your buyer client has a lender pre-approval and wants to make an offer with no financing condition so it looks stronger. What is the best advice?
A pre-approval is an estimate of what the buyer may borrow; the lender still has to approve the specific property (appraisal, title, terms). Determining financing condition requirements and due diligence is a Fundamentals learning outcome (FRE blueprint 2.2.2.5); pre-approvals are part of 'Types of Mortgages, Impact' in the PRRE glossary. Without the condition, the buyer's deposit is at risk.
25. A buyer plans to pay $500,000 with $50,000 down. The appraisal comes in at $470,000, and the lender lends up to 90% of the lower of price and appraised value. How much more cash does the buyer need beyond the $50,000?
Loan = 90% x $470,000 = $423,000. Cash needed = $500,000 - $423,000 = $77,000; minus the $50,000 already planned = $27,000. Put another way, the loan falls from $450,000 (90% of the price) to $423,000, and the buyer must make up that $27,000 difference; it is not the full $30,000 appraisal gap.
26. A $250,000 interest-only mortgage carries a rate of 6% per year. Interest is calculated monthly at the annual rate divided by 12. What is the monthly payment?
Monthly rate = 6% / 12 = 0.5%; $250,000 x 0.005 = $1,250. $15,000 is a full year of interest. On an interest-only mortgage the payment never reduces the principal (FRE blueprint 2.2.2.3, types of mortgages).
27. A $400,000 mortgage has a rate of 5.00% per year compounded semi-annually, with monthly payments. Using the equivalent monthly rate, how much interest accrues in the first month?
Semi-annual rate = 5% / 2 = 2.5%. Equivalent monthly rate = 1.025^(1/6) - 1 = 0.412392%. Interest = $400,000 x 0.00412392 = $1,649.57. Dividing 5% by 12 ($1,666.67) assumes monthly compounding; $10,000 is six months of interest.
28. A buyer takes a $360,000 mortgage amortized over 25 years at 5.5% per year compounded semi-annually, with monthly payments. What is the monthly payment of principal and interest?
Monthly rate i = 1.0275^(1/6) - 1 = 0.00453168; n = 25 x 12 = 300. Payment = P x i / (1 - (1 + i)^-300) = $2,197.41 (HP 10bII+: 12 P/YR, 300 N, I/YR = nominal monthly equivalent 5.438018, PV 360,000). Treating 5.5% as compounded monthly gives $2,210.71; $1,650 would pay interest only.
29. A borrower owes $380,000 at 4.95% per year, with interest calculated monthly at the annual rate divided by 12. The monthly payment is $2,150. How much of the first payment reduces the principal?
Interest for the month = $380,000 x 4.95% / 12 = $1,567.50. Principal = $2,150 - $1,567.50 = $582.50. $1,567.50 is the interest part of the payment, not the principal part.
30. In this scenario, a closed mortgage lets the borrower prepay up to 15% of the original principal each year without penalty. The original principal was $420,000 and the balance is now $380,000. What is the most that can be prepaid this year without penalty?
15% x $420,000 (original principal) = $63,000. Using the current balance gives $57,000. Prepayment terms distinguish closed from open mortgages (PRRE glossary, 'Types of Mortgages, Impact': open, closed, variable, assumable); the 15% figure is fictional, set in the question.
31. In this scenario, the penalty for paying off a closed mortgage early is three months' interest at the mortgage rate. The balance is $300,000 at 4.8% per year (simple interest, annual rate divided by 12). What is the penalty?
One month of interest = $300,000 x 4.8% / 12 = $1,200; three months = $3,600. $14,400 is a full year of interest. Penalty terms are fictional, set in the question; they are the kind of term a licensee asks about when a seller must discharge a mortgage (FRE blueprint 2.2.2.8).
32. A borrower's monthly payment is $2,400. She switches to accelerated bi-weekly payments, which are half the monthly payment made every two weeks (26 payments a year). How much more does she pay toward the mortgage each year?
Accelerated: $1,200 x 26 = $31,200. Monthly: $2,400 x 12 = $28,800. Difference = $2,400, i.e. one extra monthly payment a year. $1,107.69 is a regular (non-accelerated) bi-weekly payment.
33. A buyer qualifies for a $400,000 mortgage amortized over 25 years, with monthly payments and semi-annual compounding. Before she commits, the rate rises from 4% to 6%. By how much does her monthly payment rise?
At 4%: i = 1.02^(1/6) - 1, payment $2,104.08. At 6%: i = 1.03^(1/6) - 1, payment $2,559.23. Increase = $455.15. Rate changes are a market dynamic that affects affordability (FRE blueprint 2.2.2.11; PRRE 2.1.1.2). $666.67 is the change in interest only, not in the blended payment.
34. After a judicial sale, proceeds are $430,000. Costs of sale and enforcement of $18,000 are paid first. The first mortgage, registered earlier, is owed $300,000 and the second mortgage $120,000. How much does the second mortgagee receive?
Net proceeds = $430,000 - $18,000 = $412,000. The first mortgage ranks ahead by registration (Land Titles Act s.14(3), s.56): $412,000 - $300,000 = $112,000 left for the second mortgagee, who is short $8,000. Ignoring the costs would wrongly pay the second mortgage in full. The foreclosure process and its impact on a transaction is a Fundamentals outcome (FRE blueprint 2.2.2.12).
35. Mortgage A ($220,000 owing) was registered on March 3 and Mortgage B ($180,000 owing) on March 20. Lender A then registered a postponement of Mortgage A to Mortgage B. Net sale proceeds are $350,000. How much does Lender A receive?
A registered postponement ranks the postponed instrument as if it had been registered after the one it is postponed to (Land Titles Act s.107(2)). B is paid first: $180,000; A receives $350,000 - $180,000 = $170,000. Without the postponement A would be paid in full and B would get $130,000. Priority is not shared pro rata.
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