Money · Junior Cert
Money
Junior Cert Higher · Percentages, profit & compound interest · Tap NEXT to begin
Section 1 of 5
Percentages of Money
To find a percentage of an amount, turn the percent into a decimal and multiply.
Worked example — a percentage of an amount
Find $6\%$ of €$250$.
$0.06 \times 250$
€$15$
Worked example — a percentage increase
Find the value after a $3.5\%$ increase on €$240$.
A $3.5\%$ increase means $\times 1.035$
$240 \times 1.035$
€$248.40$
Worked example — a percentage decrease
Find the value after a $4\%$ decrease on €$360$.
A $4\%$ decrease means $\times 0.96$
$360 \times 0.96$
€$345.60$
Section 2 of 5
Profit, Loss & Error
The two formulas
$\%\text{ profit} = \dfrac{\text{increase}}{\text{original}}\times 100$. $\%\text{ error} = \dfrac{\text{error}}{\text{real value}}\times 100$.
Worked example — percentage profit
A coat costs €$120$ and is sold for €$180$. Find the percentage profit.
Profit $= 180 - 120 = 60$
$\%\text{ profit} = \dfrac{60}{120}\times 100$
$50\%$ profit
Worked example — percentage error
$2.33$ is rounded to $2$. Find the percentage error.
Error $= 2.33 - 2 = 0.33$
$\%\text{ error} = \dfrac{0.33}{2.33}\times 100$
$14.2\%$
Section 3 of 5
Reverse Percentages
When a price already includes a percentage, work back to $100\%$.
Worked example — a profit included
A coat is sold for €$165$, which includes a $10\%$ profit. Find the cost price.
The selling price is $110\%$ of the cost: $110\% = 165$
$1\% = \dfrac{165}{110}$, so $100\% = \dfrac{165}{110}\times 100$
cost $=$ €$150$
Now you try
You try
A car is sold at an $8\%$ profit; the profit is €$960$. Find the cost price.
Pen and paper out — try it before you reveal.
$8\% = 960$, so $1\% = \dfrac{960}{8} = 120$
$100\% = 120 \times 100$
cost $=$ €$12{,}000$
cost $=$ €$12{,}000$
Section 4 of 5
Compound Interest
The formula (in your tables)
$F = P(1+i)^{t}$: $P$ principal, $i$ rate as a decimal, $t$ years, $F$ final value.
You try
€$6200$ is invested for $3$ years at $1.8\%$ AER. Find its value at the end.
Pen and paper out — try it before you reveal.
$i = 0.018$, $t = 3$
$F = 6200(1.018)^{3}$
€$6540.86$
€$6540.86$
You try
A sum invested for $2$ years at $3.1\%$ AER is worth €$4253$. How much was invested?
Pen and paper out — try it before you reveal.
$P = \dfrac{F}{(1+i)^{t}} = \dfrac{4253}{(1.031)^{2}}$
€$4001.09$
€$4001.09$
Section 5 of 5
Loans with Repayments
Add the interest each year; subtract any repayment before the next year’s interest.
You try
€$5000$ is borrowed for $2$ years at $8\%$ APR. €$2000$ is paid back at the end of year $1$. How much is owed at the end of year $2$?
Pen and paper out — try it before you reveal.
End of year $1$: $5000(1.08) = 5400$, then pay $2000 \Rightarrow 3400$
End of year $2$: $3400(1.08)$
€$3672$
€$3672$
More examples
Worked example — a percentage increase
Find the value after a $6\%$ increase on €$275$.
$275 \times 1.06$
€$291.50$
You try
I got $52$ out of $85$ in a test. What percentage did I get (1 d.p.)?
$\dfrac{\text{score}}{\text{total}}\times 100$.
$\dfrac{52}{85}\times 100$
$61.2\%$
You try
A car is sold for €$16{,}520$, which includes a $10\%$ profit. Find the cost price.
The price is $110\%$ of the cost.
$110\% = 16520$
$100\% = \dfrac{16520}{110}\times 100$
cost $=$ €$15{,}020$
That’s Money.
Percentages, profit & error, reverse percentages, compound interest and loans — the whole of Junior Cert financial maths.