Secondary 5 Financial Mathematics Worksheet

All 9 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one.

1. Q1Compound Interest Rates

   Kenji deposits $2500 in an account paying $4\%$ per year, compounded annually. He makes no other deposit and no withdrawal for 6 years. Find the value of the account after 6 years and the total interest earned. Round to the nearest cent.

2. Q2Compound Interest Rates

   Sabrina has $4000 to place for 5 years. The Banque du Nord offers $6\%$ per year compounded quarterly; the Caisse de l'Est offers $6.1\%$ per year compounded annually. Determine which institution returns more, and by how much.

3. Q3Financial Mathematics

   Nadia deposits $1800 in an account paying a nominal rate of $3.5\%$ per year, compounded semi-annually, and leaves it for 4 years.

   1. State the capital $C$, the periodic interest rate $i$ and the number of interest periods $n$.
   2. Explain, in one or two sentences, the difference between the nominal annual rate and the periodic rate.
   3. Find the final value of the account and the interest it earned.
4. Q4Financial Mathematics

   Ophélie wants $10 000 available in 8 years for a study exchange.

   1. How much must she deposit today in an account paying $5\%$ per year compounded annually?
   2. Without computing first, predict whether she would have to deposit more or less if the same $5\%$ were compounded monthly. Then verify by computing the amount.
5. Q5Simple Interest Rates

   A community fund lends $3200 at a simple interest rate of $5.25\%$ per year for 3 years. Find the interest owed and the total amount to be repaid.

6. Q6Simple Interest Rates

   Léa borrows $1450 from a credit union at $7.2\%$ simple interest per year and repays the loan in full after 8 months. The credit union also charges a $25 file-opening fee, payable at the end with the loan.

   1. How much interest does she pay?
   2. What total amount does she hand over?
   3. What single simple annual rate, applied over the same 8 months and with no fee, would have cost her exactly the same? Round to the nearest hundredth of a percent.
7. Q7Solving Problems in Financial Mathematics

   A cooperative can place $5000 for 3 years in one of two accounts: account A pays $6.5\%$ simple interest per year, account B pays $6\%$ per year compounded annually. Which account yields more, and by how much?

8. Q8Solving Problems in Financial Mathematics

   A bakery is replacing an oven. The supplier proposes two ways to pay:

   1. pay $7200 in cash today; or
   2. pay $2000 today and $5600 in 3 years.

   The bakery's money earns $5\%$ per year compounded annually. Determine which proposal costs the bakery less, and express the saving in today's dollars.

9. Q9Synthesis — drawing on several sheets in this topic

   Étienne must have $9000 available in exactly 6 years to redo the roof of his cabin. He is considering two ways of getting there.

   1. Plan 1: a single deposit today in an account paying $4.8\%$ per year compounded semi-annually. How much must he deposit?
   2. Plan 2: depositing $7000 today in an account paying simple interest. What annual rate would that account have to pay? Round to the nearest hundredth of a percent.
   3. Which plan requires less money from him today, and by how much?

The 5 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

Two models, and knowing instantly which one you are in

Every question on this sheet uses one of two formulas, and reading which one from the wording is half the exercise. Q5 and Q6 are simple interest; Q1, Q3 and Q4 are compound; Q7 and Q9 put the two models head to head. Q2 and Q8 are comparisons that stay inside the compound model throughout — Q2 sets one compounding frequency against another, Q8 sets two payment dates against each other — so the first decision there is not which formula but which date everything will be measured at.

Under simple interest only the original capital ever earns. The same amount is added each year, so the value grows along a straight line, and the interest for t years is just C·i·t. Under compound interest the interest earned is itself added to the capital and starts earning too, so growth is exponential and the interest is A − C, never C·i·n.

The wording that gives it away: "simple interest" is always stated explicitly, and "compounded annually / semi-annually / quarterly / monthly" always signals the second model — while telling you how to build i and n.

The posted rate is not what you earn (Q2)

Q2 puts a lower rate compounded four times a year against a higher rate compounded once, and the lower one can win. That is not a trick; it is the reason effective rates exist. One year of compounding k times at periodic rate i multiplies the capital by (1 + i)ᵏ, so

Converting both offers to their effective annual rates puts them on one scale, and the comparison becomes a comparison of two numbers. It also proves the answer for every duration at once: if one growth factor is larger than the other and both exceed 1, raising both to the same power t keeps the inequality, so the better bank is better no matter how long the money stays. Answering "which is better" by computing a single term is fine when the question fixes the term, but the effective-rate argument is what makes the conclusion general.

Present value: run the formula backwards (Q4, Q8, Q9)

"How much must be deposited today to have a given amount later" is the same formula read the other way. Dividing by the growth factor is not a new technique — it is isolating C.

Q4(b) asks you to predict, before computing, whether more frequent compounding raises or lowers the deposit needed. The reasoning is short and it is the kind of sentence exams reward: more frequent compounding makes the same capital grow faster, so the growth factor you divide by is larger, so a smaller deposit suffices. The computation then confirms a prediction instead of producing an unexamined number.

When the rate is the unknown (Q6, Q9)

Twice on this sheet the money is known at both ends and the rate is what you are asked for, and both times the model is simple interest — which is good news, because A = C(1 + r·t) is linear in r. Nothing clever is needed: divide, subtract the 1, divide by the time.

Q9(b) is that formula used directly, with the deposit known and the target known. Q6(c) reaches the same algebra from a different angle: there the amount you must reproduce is not handed to you but assembled first, and the section on simple interest below is about how.

Two habits keep these honest. Convert the term to years before it enters the formula, and give the answer as a percentage rounded the way the question asks — an answer left as a decimal is an unfinished answer when the wording says "to the nearest hundredth of a percent". Then check it by running the rate forwards: if it does not rebuild the amount you started from, the slip is almost always the time.

Simple interest, and the traps that live in the wording (Q5, Q6)

The formula is easy; the reading is not. Two things to watch:

Time must be in years. A rate quoted per year and a term given in months means converting: eight months is 8/12 of a year. Leaving t = 8 in the formula multiplies the interest by twelve.

A fee is not interest, but it is a cost. Q6 adds a flat file-opening fee and then asks what single rate, with no fee, would have cost the same. The method is to total the real cost of borrowing — interest plus fee — and solve C·r·t = that total for r. The result is startling and it is the point of the question: a small fixed fee spread over a short term raises the true annual cost by several percentage points, because the fee does not shrink when the loan is short.

Which model wins depends on how long you wait (Q7, Q9)

Q7 pits a higher simple rate against a lower compound one over a short term, and the simple account can come out ahead. Compounding is a slow advantage: in the first period the two models earn identically, and the compound account only pulls away as the interest-on-interest accumulates. Over a long enough horizon compounding always wins, because exponential growth eventually beats linear growth for any positive rate — but "eventually" may be well past the term in the question.

So the method for any comparison question is the same three lines: compute each option separately, compare, and state the difference in dollars and the reason. An answer that names the winner without the reason is half an answer; Q9(c) in particular is asking for the sentence, not just the subtraction.

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Getting the most out of it

Write C, i and n in a column before you touch the calculator

Three short lines, every time, even on a question that looks obvious. Almost every lost mark on this sheet is a periodic rate that was never divided or a count of periods that was never multiplied, and both become visible the moment they are written down separately.

Keep six decimals in the growth factor, round only the money

A factor rounded to three decimals and then applied to thousands of dollars shifts the answer by more than the cent the question asks for. Carry the factor at full precision, and round once, at the end, to the nearest cent.

Predict before you compute

Q4(b) asks for this explicitly, and it is worth doing on every question: will the answer be bigger or smaller, and why? A prediction that the computation contradicts tells you immediately that something is wrong — which is far better than a plausible wrong number you never questioned.

Common questions