Year 6 Maths Money & Financial Maths

Saving goals & interest

Q: How much is 10% interest on $350?

$35, so the balance becomes $385.

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Theory

A savings goal is an amount you want to have by a certain time. A plan says how much to save each week and for how long. Money kept in a bank can also earn interest: extra money the bank pays you. This Year 6 maths page shows how to plan savings, track income and expenses, compare plans and work out one year of interest.

A savings plan has a goal (how much), a time (how long) and a regular amount (how much each week or month).

Weeks needed $=$ goal $\div$ amount saved each week (round up to a whole week). Amount each week $=$ goal $\div$ number of weeks.

A need is something you must have (food, rent, electricity). A want is nice to have (games, concert tickets). Pay for needs first.

Income is money coming in; expenses are money going out. Profit $=$ income $-$ expenses.

Interest is money a bank adds to your savings. $10\%$ interest for a year on $\$350$ is $\$35$, so the balance grows to $\$385$.

Saving $\$12$ a week, the total first passes $\$90$ in week $8$.

$10\%$ of $\$350$ is $\$35$, so the balance is $\$385$.

Profit $= \$360 - \$95 - \$50 = \$215$.

Saving and interest:

\[ \text{weeks} = \text{goal} \div \text{weekly saving} \]

weeks = goal \div weekly saving

\[ \text{weekly saving} = \text{goal} \div \text{weeks} \]

weekly saving = goal \div weeks

\[ \text{profit} = \text{income} - \text{expenses} \]

profit = income - expenses

\[ \text{new balance} = \text{savings} + \text{interest} \]

new balance = savings + interest

Interest rate	On $\$800$	On $\$600$
$1\%$	$\$8$	$\$6$
$5\%$	$\$40$	$\$30$
$10\%$	$\$80$	$\$60$

          Round up the weeks. If \(\$90 \div \$12 = 7.5\), you need \(8\) weeks: after \(7\) weeks you are still short.
        

          Three questions before buying. Do I need it? Can I afford it? How much do I need to save?
        

How to make a savings plan

Write the goal and subtract anything already saved.
Divide by the weekly amount to find the weeks (round up), or by the weeks to find the weekly amount.
Check with a tracker table or graph.

How to find one year of interest

Find the percentage of the amount saved ($10\%$: divide by $10$; $1\%$: divide by $100$; $5\%$: half of $10\%$).
Add the interest to the savings for the new balance.

Example 1 — Weeks to save

Ruby wants a $\$84$ scooter. She saves $\$12$ a week. How many weeks will it take?

Solution

$84 \div 12$

$=$

$7$

84 \div 12 = 7

$7$ weeks.

Example 2 — Amount each week

Tom wants $\$150$ for a guitar in $6$ weeks. How much must he save each week?

Solution

$150 \div 6$

$=$

$25$

150 \div 6 = 25

$\$25$ a week.

Example 3 — Needs and wants

Sort into needs and wants: groceries, concert tickets, rent, a new video game.

Solution

Needs: groceries, rent. Wants: concert tickets, a new video game.

Example 4 — Interest in dollars

Kai has $\$250$ in the bank. After one year the bank pays $\$6$ interest. What is his balance?

Solution

$250 + 6$

$=$

$256$

250 + 6 = 256

$\$256$.

Example 5 — Interest as a percentage

(i) A bank pays $10\%$ interest for a year on $\$350$. What is the new balance?
(ii) How much interest is $5\%$ of $\$600$?

Solution

$350 \div 10$	$=$	$35$
$350 + 35$	$=$	$385$
$600 \div 10 \div 2$	$=$	$30$

3538530

(i) $\$385$
(ii) $\$30$

Example 6 — Compare two plans

Plan A: save $\$7$ a week for $10$ weeks. Plan B: save $\$25$ a month for $3$ months. Which saves more, and by how much?

Solution

$7 \times 10$	$=$	$70$
$25 \times 3$	$=$	$75$
$75 - 70$	$=$	$5$

707575 - 70 = 5

Plan B, by $\$5$.

Example 7 — Fundraiser

A class sells $120$ sausages at $\$3$ each. Expenses are $\$145$. The camp goal is $\$250$.
(i) What is the profit?
(ii) How much short of the goal are they?

Solution

$120 \times 3$	$=$	$360$
$360 - 145$	$=$	$215$
$250 - 215$	$=$	$35$

360 - 145 = 215250 - 215 = 35

(i) $\$215$
(ii) $\$35$ short

Example 8 — Spend some, save the rest

Mila gets $\$20$ a week, spends $\$8$ and saves the rest. How many weeks until she can buy a $\$90$ watch?

Solution

$20 - 8$	$=$	$12$
$12 \times 7$	$=$	$84$
$12 \times 8$	$=$	$96$

12 a week 84 after 7 weeks 96 after 8 weeks

$\$84$ is not enough, so $8$ weeks (see the graph).

Example 9 — Bank or money box?

Sam has $\$700$. A bank pays $5\%$ interest for one year. How much more will he have after a year than if he keeps it in a money box?

Solution

$700 \div 10 \div 2$

$=$

$35$

700 \div 10 \div 2 = 35

$\$35$ more ($\$735$ against $\$700$). The money is also safer in a bank.

Example 10 — Plan falls behind

Ella plans to save $\$20$ a week for $12$ weeks to reach $\$240$. After $6$ weeks she spends $\$30$ of her savings on a school excursion. How much must she save each week for the last $6$ weeks?

Solution

$20 \times 6 - 30$	$=$	$90$
$240 - 90$	$=$	$150$
$150 \div 6$	$=$	$25$

90 saved 150 still needed 150 \div 6 = 25

$\$25$ a week.

Common pitfalls

Rounding the weeks down. $7.5$ weeks means $8$ weeks; after $7$ weeks there is not enough.

Forgetting money already saved. Subtract what you already have from the goal before dividing.

Treating interest as the new balance. Interest is the extra; add it to the savings: $\$350 + \$35$.

Profit equals income. Subtract all the expenses from the income to find the profit.

Frequently asked questions

What is a savings goal?

An amount of money you plan to have saved by a certain time.

How do I work out how many weeks to save?

Divide the amount still needed by the amount saved each week, and round up.

What is interest?

Extra money a bank pays you for keeping your savings there.

How much is $10\%$ interest on $\$350$?

$\$35$, so the balance becomes $\$385$.

What is the difference between a need and a want?

A need is something you must have; a want is nice to have but not necessary.

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Interest rate	On \(\$800\)	On \(\$600\)
\(1\%\)	\(\$8\)	\(\$6\)
\(5\%\)	\(\$40\)	\(\$30\)
\(10\%\)	\(\$80\)	\(\$60\)

\(350 \div 10\)	\(=\)	\(35\)
\(350 + 35\)	\(=\)	\(385\)
\(600 \div 10 \div 2\)	\(=\)	\(30\)

\(7 \times 10\)	\(=\)	\(70\)
\(25 \times 3\)	\(=\)	\(75\)
\(75 - 70\)	\(=\)	\(5\)

\(120 \times 3\)	\(=\)	\(360\)
\(360 - 145\)	\(=\)	\(215\)
\(250 - 215\)	\(=\)	\(35\)

\(20 - 8\)	\(=\)	\(12\)
\(12 \times 7\)	\(=\)	\(84\)
\(12 \times 8\)	\(=\)	\(96\)

\(20 \times 6 - 30\)	\(=\)	\(90\)
\(240 - 90\)	\(=\)	\(150\)
\(150 \div 6\)	\(=\)	\(25\)

Saving goals & interest

📖 Theory

How to make a savings plan

How to find one year of interest

Common pitfalls

Frequently asked questions

Theory