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B2.4 · Investigate how investment conditions affect future value

Learn to investigate how investment conditions affect future value through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Saving, Investing, and Borrowing

MEL3E study topic B2.4: compare the effects of investment choices using repeated calculations

Imagine that you have saved money from a part-time job and want to leave it in an account for a few years. The amount you have later is its future value: the money in the account at a chosen time in the future. Investment conditions are the choices and rules that affect how that amount grows. These can include the starting deposit, the interest rate, how long the money stays invested, and how often interest is added. In this lesson, you will change one condition at a time and use repeated calculations to see what happens. This makes comparisons fair and helps you explain your decision.

What you will learn

Describe how an investment’s starting amount, interest rate, time, and interest schedule can affect its future value.
Use repeated calculations or a spreadsheet to find and compare future values.
Explain why a particular investment condition leads to a higher or lower future value.

1. Read the investment conditions

The starting deposit is the amount first put into the investment. The interest rate is the rate used to work out the interest for a stated time, such as a year. Interest is money earned for letting the financial institution use your money. The investment term is how long the money stays invested.

A simple comparison changes only one condition at a time. For example, compare two accounts with the same starting deposit and term, but different annual interest rates. If the conditions are otherwise the same, the difference in future value shows the effect of the rate.

Interest may be added to the account at different times. When interest is added, it becomes part of the balance used for the next interest calculation. This means later interest may be calculated on earlier interest as well as on the original deposit. The schedule matters because interest added sooner can begin contributing to later balances sooner.

An account’s posted rate is not the only detail to check. Look for how often interest is added and whether the stated rate is annual. Use the same time period and the same assumptions when comparing offers. If an account has fees or other conditions that affect the balance, include them when reliable information is available; otherwise, state that they are not included.

Future value is the account balance at a chosen future time.
For a fair comparison, hold conditions steady except for the one being investigated.
Check both the rate and the schedule for adding interest.

2. Build the future value one period at a time

A period is one step in the account’s interest schedule. If interest is added once each year, one period is one year. Begin with the current balance. Find the interest for that period, add it to the balance, and use the new balance for the next period.

For example, with a balance of CAD 200 and annual interest of 5%, one year’s interest is CAD 10 because 5% of CAD 200 is CAD 10. The balance after that year is CAD 210. If another year passes under the same conditions, the interest is worked out using CAD 210, not just the original CAD 200.

A calculator is useful for checking each step. A spreadsheet can keep the work organized. Put the period number in one column, the starting balance in another, the interest earned in a third, and the ending balance in a fourth. The ending balance for one row becomes the starting balance for the next row. Keep enough decimal places during calculations, then round the final amount to the nearest cent.

When comparing investment conditions, make a small plan before calculating: write down the starting amount, rate, length of time, and schedule for each option. If the options have different schedules, use the stated schedule for each one. Do not compare an annual result for one option with a monthly result for another unless both results cover the same length of time.

\text{ending balance}

\text{starting balance}

+ interest for the period

Calculate interest on the balance for the period, then add it.
Carry each ending balance forward as the next starting balance.
Use a calculator or spreadsheet to reduce repeated arithmetic errors.

3. Investigate one condition at a time

The starting amount affects future value because interest is calculated from the balance. With the same rate, schedule, and term, a larger starting deposit will generally lead to a larger ending balance. A larger deposit does not mean the account has a better rate; it means more money was invested at the beginning.

The interest rate also matters. With the same starting amount, schedule, and term, a higher rate generally produces a higher future value. The difference can grow over time because interest added to the balance can earn interest in later periods.

Time matters too. If the other conditions stay the same, leaving the money invested for more periods gives it more chances to earn interest. This is why a useful comparison states the term clearly, rather than only giving an interest rate.

The interest schedule can affect the result. If the same annual rate is applied and interest is added more often, interest may become part of the balance sooner. Repeated calculations can show the effect without relying on a shortcut formula: follow each account’s schedule and compare the balances after the same total time.

Do not conclude that one condition is always best in every real situation from a calculation alone. This investigation compares future values based on the conditions provided. Access to the money, fees, and other account rules may also matter to a person making a real choice.

A higher starting deposit, higher rate, or longer term can raise future value when other conditions are held steady.
The schedule can change when interest joins the balance.
State what stayed the same and what changed before drawing a conclusion.

4. Use a clear comparison to make a decision

A good comparison includes more than two final numbers. Show the important conditions, calculate the future values over the same total time, and explain the reason for the difference. Use the table or notes from the calculation to check that you have not accidentally changed more than one condition.

If the calculated balances are close, describe the difference accurately instead of calling one choice much better. If information is missing, such as how often interest is added, do not guess. Ask for that condition or explain that the comparison cannot yet be completed.

Your conclusion should connect the result to the condition you investigated. For instance: “With the same starting deposit and two-year term, the account with the higher annual rate ends with more because each period earns more interest.” This is a supported conclusion because it names what was held steady and what caused the change.

Compare balances at the same future date.
Use the calculation and the stated conditions to support your conclusion.
Identify missing details rather than making assumptions.

A spreadsheet layout for repeated calculations

Period	Starting balance	Interest for period	Ending balance
1	The original deposit	The period’s rate applied to starting balance	Starting balance plus interest
2	Period 1 ending balance	The period’s rate applied to starting balance	Starting balance plus interest
Next period	Previous period’s ending balance	The period’s rate applied to starting balance	Starting balance plus interest

Worked example

Example 1: Compare two annual rates

A student invests CAD 500 for three years. Account A pays 3% annual interest, added once each year. Account B pays 4% annual interest, added once each year. There are no deposits or withdrawals. Which account has the greater future value?

Set up the comparison
Both accounts begin with the same amount, use the same yearly schedule, and last three years. Only the annual rate changes, so this comparison investigates the effect of the rate.
Calculate Account A
For each year, find the stated percent of the current balance and add it. Carry the ending balance into the next year. Keep the unrounded amounts during the repeated calculations.
$500\times1.03=515;\quad 515\times1.03=530.45;\quad 530.45\times1.03=546.3635$
Calculate Account B
Repeat the same process using 4% each year. Multiplying by 1.04 is a convenient way to add 4% of the current balance, but the calculation is still being repeated for each year.
$500\times1.04=520;\quad 520\times1.04=540.80;\quad 540.80\times1.04=562.432$
Compare the rounded balances
Round each final balance to the nearest cent. Account B has the greater future value because its higher annual rate adds more interest over the same term.
$\text{A: CAD }546.36;\quad \text{B: CAD }562.43$

Answer: Account B has the greater future value: CAD 562.43 compared with CAD 546.36 for Account A.

Check: The starting deposit and term match, and each account uses the same annual schedule. Account B’s balance is higher after every year, which fits the higher rate.

Worked example

Example 2: Compare how often interest is added

Two accounts each receive a CAD 1,000 deposit for one year and have a stated annual rate of 6%. Account C adds interest once at the end of the year. Account D adds interest every six months, using half the annual rate each six months. There are no other deposits or withdrawals. Compare their one-year future values.

Find Account C’s balance
Account C has one interest period for the year. Six percent of CAD 1,000 is CAD 60, so add CAD 60 to the starting balance.
$1{,}000+60=1{,}060$
Find Account D’s first period
A half-year uses half of the stated annual rate, which is 3%. Find 3% of the starting balance and add it. This gives the balance after the first six months.
$1{,}000\times1.03=1{,}030$
Find Account D’s second period
The second six-month interest amount is based on the updated balance of CAD 1,030. Add 3% of that balance to find the amount after one full year.
$1{,}030\times1.03=1{,}060.90$
Interpret the result
The two accounts have the same starting deposit, stated annual rate, and one-year term. Under the conditions given, Account D ends with CAD 0.90 more because the first half-year’s interest is included when the second period’s interest is calculated.
$1{,}060.90-1{,}060=0.90$

Answer: Account D has the greater one-year future value: CAD 1,060.90, compared with CAD 1,060.00 for Account C.

Check: Account D earns CAD 30 in the first half-year and CAD 30.90 in the second. The second amount is larger because it is calculated on CAD 1,030.

Common mistakes and how to avoid them

Using the original deposit to calculate interest in every period.

Correction: Use the balance at the start of that period. Earlier interest may already be part of the balance.

Comparing two accounts with different terms and saying the rate alone caused the difference.

Correction: Name every condition that changed. To investigate the rate alone, keep the deposit, schedule, and term the same.

Rounding every intermediate balance to cents.

Correction: Keep extra digits during repeated calculations and round the final balance to cents. This avoids small rounding differences building up.

Treating a stated annual rate as a rate for every month or half-year.

Correction: Read the account conditions. Use the rate for the period as stated; do not apply the full annual rate to a shorter period.

Lesson summary

Future value is the balance at a chosen future time.
To calculate it, find interest for one period, add it, and carry the new balance forward.
Use a calculator or spreadsheet to repeat the process accurately.
A useful investigation changes one condition at a time and compares balances at the same future date.
Explain how the changed condition accounts for the difference in future value.

Check your understanding

Question 1

Two accounts have the same CAD 800 starting deposit, annual schedule, and two-year term. One pays 2% annually and the other pays 3% annually. Which statement is supported?

The 3% account should have the greater future value because its rate is higher while the other conditions match.
The 2% account must have the greater future value because it has a lower rate.
The accounts must have the same future value because their starting deposits match.
correctIndexи

Show answer and explanation

The 3% account should have the greater future value because its rate is higher while the other conditions match.

With the other conditions held steady, the higher rate adds more interest in each period. The starting deposits being equal does not make the final balances equal.

Question 2

An account starts with CAD 400. It earns 5% for the first year, then 5% for the second year, with interest added annually. What balance does it have after the first year?

CAD 405
CAD 420
CAD 440
correctIndex

Show answer and explanation

CAD 420

Five percent of CAD 400 is CAD 20. Adding the interest gives CAD 420.

Key terms

Future value: The amount in an investment account at a chosen future time.
Interest: Money earned on an investment balance.
Interest rate: The stated percent used to calculate interest for a stated time.
Investment term: The length of time the money stays invested.
Period: One step in the schedule used to add interest, such as one year or six months.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation B2.4. It is a study resource, not an official curriculum publication.

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