BC Real Estate Exam Math Practice: 8 Mortgage Questions Worked Step by Step

Before you start: two settings that decide everything

Every problem below assumes an HP 10bII+ set up the way the course expects: P/YR set to 12 for monthly payments (and changed deliberately when you convert rates), END mode (payments at the end of each period, which is how mortgages work), and the sign convention that money you receive is positive and money you pay is negative. If a payment shows up as a negative number, that is the calculator telling you the direction of the cash flow, not an error.

Every answer below was checked with full calculator precision. If yours differs by a cent, you rounded the converted rate before using it. Never round the rate: convert it, store it in the calculator, and go straight to the next step.

The formulas behind each step are in our exam math formulas post, and the keystroke walkthrough is in the HP 10bII+ mortgage math guide. This post is the practice.

Question 1: the monthly payment

A $350,000 mortgage at 4.5% per annum, compounded semi-annually, amortized over 25 years with monthly payments. What is the payment?

Step 1, convert the rate. The rate is compounded twice a year; payments happen twelve times a year. Set P/YR to 2, enter 4.5 as NOM%, compute EFF% (the effective annual rate, 4.5506%). Now set P/YR to 12 and compute NOM% from that effective rate: 4.4584%. That is the nominal rate compounded monthly that is equivalent to 4.5% compounded semi-annually. Leave it in the calculator.

Step 2, solve for the payment. N = 300 (25 years times 12), I/YR is the converted rate already sitting there, PV = 350,000, FV = 0. Solve PMT.

Answer: $1,937.16 per month (displayed as a negative, because you pay it).

Skip the conversion and use 4.5% straight, and the calculator gives $1,945.41. That eight-dollar difference is the whole mark, and on the exam one of the wrong options will be exactly that number.

Question 2: rate conversion on its own

A lender quotes 5.2% per annum compounded semi-annually. What is the equivalent nominal rate compounded monthly, and what is the effective annual rate?

Keystrokes. P/YR = 2, NOM% = 5.2, compute EFF%: 5.2676%. Then P/YR = 12, compute NOM%: 5.1445%.

Why the monthly nominal rate is lower. Compounding more often at the same nominal rate would produce more interest. To produce the same interest with monthly compounding, the nominal rate has to come down a little. If your converted monthly rate is ever higher than the semi-annual one, you have the direction backwards. The interest rate conversion post has more drills on exactly this.

Question 3: outstanding balance

Using the mortgage from Question 1 (payment $1,937.16), what is the outstanding balance immediately after the 60th payment, at the end of year five?

Method one, amortization keys. With the loan still in the calculator, use the amortization function for payments 1 through 60 and read the remaining balance.

Method two, the FV trick, which works on any financial calculator. Keep I/YR and PMT as they are, set N = 60, PV = 350,000, and solve for FV. The result is the balance still owed after 60 payments.

Answer: $307,287.04.

Notice how little has been repaid: about $42,700 of principal in five years on a $350,000 loan. That is normal for the front end of a 25-year amortization, and it is a fact the exam likes to test in words as well as in numbers.

Question 4: interest paid over a period

On the same mortgage, how much interest was paid during the first five years?

Method. Total paid over 60 months is 60 times $1,937.16, which is $116,229.60. Principal repaid is the original balance minus the balance after 60 payments: $350,000 minus $307,287.04, which is $42,712.96. Interest is what is left.

Answer: $73,516.64 of interest in the first five years.

The pattern to remember: interest paid over a period equals total payments minus the reduction in principal. The amortization keys give the same split directly, but knowing the arithmetic means you can sanity-check the calculator's answer, and sanity checks are what catch keystroke slips.

Question 5: how much can they borrow?

A borrower can afford a monthly payment of $2,200. The lender offers 5.75% per annum compounded semi-annually, amortized over 25 years. What is the maximum loan?

Step 1. Convert 5.75% semi-annual to its monthly equivalent (P/YR 2, NOM% 5.75, compute EFF%, then P/YR 12, compute NOM%: 5.6823%).

Step 2. N = 300, PMT = 2,200 (entered as a negative, because they pay it), FV = 0, solve PV.

Answer: about $351,988.

This is the same equation as Question 1 solved for a different unknown, and the exam uses that deliberately: if you understand that PV, PMT, N and I/YR are one relationship with four knobs, every variation is the same problem.

Question 6: the amortization period

A $300,000 mortgage at 4% per annum compounded semi-annually has a monthly payment of $1,900. How long will it take to pay off?

Step 1. Convert the rate: 4% compounded semi-annually is 3.9671% compounded monthly.

Step 2. PV = 300,000, PMT = 1,900 (negative), FV = 0, solve N.

Answer: about 223.6 months, which is 18.6 years. In words: paying $1,900 a month instead of the 25-year payment shortens the amortization by more than six years.

The exam sometimes asks this the other way around: "what payment is needed to pay the loan off in 15 years?" Same equation, solve PMT with N = 180.

Question 7: effective annual rate

A line of credit charges 6% per annum compounded monthly. What is the effective annual rate?

Keystrokes. P/YR = 12, NOM% = 6, compute EFF%.

Answer: 6.1678%.

The concept: 6% compounded monthly is half a percent a month, and twelve rounds of half a percent compound to a little more than 6%. When a question compares two rates with different compounding frequencies, convert both to effective annual rates and compare those. That is the only fair comparison, and it is the comparison the exam wants.

Question 8: a qualifying ratio

A household earns $96,000 a year. If a lender uses a 32% gross debt service ratio, what is the maximum monthly housing cost (mortgage payment, property taxes and heating) the household can carry?

Method. Annual income times the ratio, divided by twelve: $96,000 times 0.32 is $30,720 a year, which is $2,560 a month.

Lenders' ratio limits change with policy, so a question will always give you the ratio to use. What the exam tests is that you know what goes in the numerator (principal, interest, taxes, heat, and typically half of strata fees) and that you divide by gross income, not net.

Where people actually lose the marks

Across all eight questions, the errors that cost marks are the same three every time:

1. Not converting the rate, or converting it and then rounding it before using it.
2. Sign errors, entering PV and PMT with the same sign and getting a nonsense answer or no answer at all.
3. Leaving a stale value in a register, usually FV or N from the previous problem. Clear the time value of money registers between questions, every time.

None of these are knowledge gaps. They are habits, and habits are built by repetition. Ten minutes a day on problems like these for the last four weeks before your exam turns the math from the section that fails people into the section that carries them.

Practise with the full drill set

These eight problems are the shape of the math section. The full set, with the calculator course that teaches every keystroke and quizzes that tell you exactly which step you are getting wrong, is inside RealtyPrep. Try Chapter 1 free to see how the lessons work, or start with a free practice exam. The Exam Pass includes the complete calculator course and unlimited mock exams, backed by a pass-or-refund guarantee.