27 topics
Financial math help, from compound interest to amortisation
Financial math is arithmetic with a timeline attached, and almost every wrong answer traces back to the timeline rather than the formula. A payment made at the start of a period and the same payment made at the end are different numbers. The rate quoted on a loan is rarely the rate at which the money actually grows. Get those two straight and most of the course follows.
Where students get stuck
Nominal, periodic, effective — the rate in the question is never the rate I need
Sort the rate out before you touch a formula. A rate quoted annually but compounded monthly is nominal: divide by twelve to get the periodic rate and use that alongside a count of months, never years. The effective annual rate is what one dollar genuinely becomes over a year, and it is the only rate that lets you compare two products with different compounding. Canadian mortgages add a wrinkle worth knowing: they are quoted with semi-annual compounding but paid monthly, so you have to convert to an equivalent monthly rate first. Wrong period, wrong answer, every single time.
Ordinary annuity or annuity due — I keep choosing the wrong one
Draw the timeline and mark where the payments actually sit. An ordinary annuity pays at the end of each period, which is how loans and most bond coupons work. An annuity due pays at the beginning, which is how rent, leases and many savings plans work. You do not need a second formula for it: an annuity due is worth exactly one plus the periodic rate, times the ordinary annuity value, because every payment has moved one period earlier and picks up one more period of interest. Learn one formula and that multiplier and the pair stops being confusing.
Why is almost none of my mortgage payment going to the principal?
Because interest is charged on what you still owe, and at the beginning you still owe nearly all of it. Each payment is split by working out the interest on the current balance first; only what is left over reduces the principal. On a 300,000 dollar loan at 5 percent, the first month of interest is roughly 1,250 dollars, so a 1,750 dollar payment retires about 500 dollars of debt. As the balance falls the interest portion falls with it and the principal portion grows, which is why an amortisation schedule curves rather than running in a straight line, and why one extra payment early saves far more than the same payment made near the end.
NPV and IRR disagree about which project to choose
When they disagree, trust net present value. NPV discounts every cash flow at the rate you actually pay for money and tells you how much value the project adds in dollars. Internal rate of return solves for the discount rate that would make that value zero, which is a comparison shortcut and nothing more. It breaks in two known ways. If the cash flows change sign more than once there can be several internal rates, all of them technically correct and none of them useful. And it ignores scale, so a tiny project with a spectacular percentage can beat a large project that adds far more money. Rank by NPV and quote IRR beside it.
What's covered
Financial Math topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Interest and the time value of money
- Simple and compound interest
- Nominal, periodic and effective rates
- Present value and future value
- Compounding frequency and continuous compounding
- Inflation and real rates of return
Annuities and loans
- Ordinary annuities and annuities due
- Present and future value of an annuity
- Deferred annuities and perpetuities
- Calculating a loan payment
- Amortisation schedules
- Outstanding balance and early repayment
Investments
- Bonds, coupons and yield to maturity
- Stocks, dividends and total return
- Mutual funds, index funds and fees
- Risk, return and diversification
- Registered accounts in Canada: RRSP, TFSA and RESP
Capital budgeting
- Cash flow diagrams
- Net present value
- Internal rate of return
- Payback period
- Comparing projects of unequal length
Personal and business finance
- Credit cards and minimum payments
- Mortgages, terms and renewals
- Leasing versus buying
- Payroll deductions and basic income tax
- Budgeting and savings goals
- Currency conversion
Financial Math questions
Is this the Grade 11 and 12 financial math unit, or a university finance course?
Both are in the list above. The high school unit lives in the interest, annuity and personal finance groups. A first university course adds bonds, yield to maturity and capital budgeting, and expects the derivations rather than the formula sheet. Say which and it will stay at that depth.
Can you tell me which investment I should actually put my money in?
No. Nothing here is financial advice and it will not recommend a product, a fund or a stock. What it will do is the mathematics: what a given rate compounds to, what a fee costs you over twenty years, what two loan offers really cost side by side. The decision stays with you and a licensed advisor.
Can it build an amortisation schedule with me instead of just giving me the formula?
Yes. On the whiteboard it sets out the columns, computes the first month with you, then does the second so you can watch the interest portion shrink. Once the pattern is visible the rest of the table is mechanical, and questions about the balance after five years stop being guesswork.
Can I use my own real numbers, like the loan statement I actually have?
You can hold the statement up to the camera or share your screen and work through it. Be sensible about what you show — cover the account number, keep to the rate, balance and payment. Working with a real statement is usually the moment the compounding rules finally stick.
Stuck on financial math right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
Start free — no card