Sec 2 · G1 (N(T))

Money matters

Practise money matters with step-by-step help. Free account.

1. Simple interest

Symbol	Meaning	Example
$P$	principal: the amount deposited or borrowed	$ $2000$
$R$	rate, in % per year (per annum)	$3$
$T$	time, in years	$4$
$I$	interest	$ $240$

Simple interest

\displaystyle I = \dfrac{PRT}{100}

e.g.

\displaystyle I = \dfrac{2000 \times 3 \times 4}{100}

\displaystyle I = 240

Total amount: principal + interest

\displaystyle A = P + I

e.g.

\displaystyle A = 2000 + 240

\displaystyle A = 2240

Time in months: change to years first

\displaystyle T = \dfrac{\text{months}}{12}

e.g.

\displaystyle T = \dfrac{18}{12}

\displaystyle T = 1.5

📖 Worked example

Chen Wei puts $1,000 in a fixed deposit account that pays 1.5% per annum simple interest. Find the total amount in the account after 4 years.

Step 1 of 2

Substitute P, R and T into the formula

I = \dfrac{PRT}{100}

I = \dfrac{1000 \times 1.5 \times 4}{100}

= 60

📖 Worked example

Mei Ling deposits some money in a bank that pays simple interest of 2% per annum. After 5 years, the interest earned is $100. Find the amount of money Mei Ling deposited.

Step 1 of 2

Put the numbers you know into the formula

I = \dfrac{PRT}{100}

100 = \dfrac{P \times 2 \times 5}{100}

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2. GST, service charge and discounts

A $50.00 restaurant bill: a 10% service charge of $5.00 makes $55.00, then 9% GST on $55.00 is $4.95, making $59.95.

Charge	Multiply by	Example
$10\%$ service charge	$1.10$	$50 \times 1.10$ , so $ $55$
$9\%$ GST	$1.09$	$55 \times 1.09$ , so $ $59.95$
$15\%$ discount	$0.85$	$80 \times 0.85$ , so $ $68$

Restaurant bill: service charge first, then GST on that total

\displaystyle 50 \times 1.10 \times 1.09

e.g.

\displaystyle 50 \times 1.10 \times 1.09

\displaystyle = 59.95

Discount first, then GST

\displaystyle 80 \times 0.85 \times 1.09

e.g.

\displaystyle 80 \times 0.85 \times 1.09

\displaystyle = 74.12

Price before GST: the price with GST is 109%

\displaystyle 109\% \to 218

e.g.

\displaystyle \dfrac{218}{109} \times 100

\displaystyle = 200

the price before GST is $200

📖 Worked example

The table shows the food a family ordered at a restaurant. A 10% service charge is added to the bill, and then 9% GST is charged on the total. Find the amount the family pays, correct to the nearest cent.

Item	Price
Fried rice	$8.50
Iced lemon tea	$3.20
Chilli crab	$48.00

Step 1 of 3

Add up the bill (in dollars)

8.50 + 3.20 + 48.00 = 59.70

📖 Worked example

The price of an air-conditioner, including 9% GST, is $446.90. Find its price before GST.

Step 1 of 3

The price with GST is what percentage of the price before GST? (in dollars)

100\% + 9\% = 109\%

109\% \rightarrow 446.90

📖 Worked example

The table shows the food a family ordered at a restaurant. Members get a 15% discount on the food, then a 10% service charge is added, and then 9% GST is charged on the total. The family are members. Find the amount they pay, correct to the nearest cent.

Item	Price
Chicken rice	$7.60
Tom yum soup	$11.80
Roti prata set	$6.60

Step 1 of 4

Add up the food (in dollars)

7.60 + 11.80 + 6.60 = 26

Practise this →

3. Utilities and bills

Bill	Charged for	How
electricity	kWh used	current reading $-$ previous reading, $\times$ the rate
water	m³ used, in tiers	the first part at the lower rate, the rest at the higher rate
mobile phone	minutes over the free time	monthly fee $+$ extra minutes $\times$ the rate

Electricity: units used

\displaystyle 24805 - 24315

e.g.

\displaystyle 24805 - 24315

\displaystyle = 490

at $27.5$ cents per kWh: $490 \times 27.5$ is $13\,475$ cents, which is $134.75

Water: 45 m³, the first 30 m³ at $1.20, the rest at $1.60

\displaystyle 30 \times 1.20 + 15 \times 1.60

e.g.

\displaystyle 30 \times 1.20 + 15 \times 1.60

\displaystyle = 60

📖 Worked example

The table shows a household's electricity meter readings for a month and the rate charged. Find the cost of the electricity used, in dollars.

Previous meter reading	Current meter reading	Rate
12460 kWh	12828 kWh	30 cents per kWh

Step 1 of 3

Units used = current reading − previous reading

12828 - 12460 = 368 \text{ kWh}

📖 Worked example

Mei Ling's mobile phone plan is shown in the table. In March, Mei Ling made 380 minutes of calls. Find the amount of Mei Ling's bill for March.

Monthly fee	Free talk time	Extra calls
$20	300 min	10 cents per min

Step 1 of 3

Extra minutes = minutes used − free minutes

380 - 300 = 80 \text{ min}

Practise this →

4. Currency exchange

A conversion graph of yen against Singapore dollars, a straight line through the origin: S$150 reads across to ¥16 200, and ¥10 800 reads down to S$100.

Rate	S$ to the foreign currency	Back to S$
S$1 buys ¥108	multiply by $108$	divide by $108$
1 ringgit costs S$0.30	divide by $0.30$	multiply by $0.30$

S$200 into yen

\displaystyle 200 \times 108

e.g.

\displaystyle 200 \times 108

\displaystyle = 21600

¥ $21\,600$

¥16 956 back into Singapore dollars

\displaystyle \dfrac{16956}{108}

e.g.

\displaystyle \dfrac{16956}{108}

\displaystyle = 157

S$157

📖 Worked example

The table shows a money changer's exchange rates. Devi changes S$800 into Malaysian ringgit. Find the amount, in Malaysian ringgit, that Devi receives. Give your answer correct to 2 decimal places where necessary.

Currency	S$1 buys
Malaysian ringgit (RM)	3.4
Japanese yen (¥)	108
Australian dollars (A$)	1.2

Step 1 of 1

Use the exchange rate: multiply or divide?

800 \times 3.4

= 2720

Devi receives RM 2720.

📖 Worked example

Siti wants to change S$1000 into Malaysian ringgit. The rates at two money changers are shown in the table. Which money changer gives Siti more Malaysian ringgit?

Money changer	Rate
A	S$1 = RM 3.4
B	S$100 = RM 346.8

Step 1 of 3

Money changer A: the amount of Malaysian ringgit received

\text{A: } 1000 \times 3.4 = 3400

Practise this →

5. Instalments and hire purchase

Term	Meaning	Example
cash price	the price paid all at once	$ $1200$
deposit	paid at the start	$25\%$ of $1200$ : $ $300$
loan (balance)	cash price $-$ deposit	$ $900$
instalments	equal monthly payments	$30 \times 36$ : $ $1080$
hire-purchase price	deposit $+$ all the instalments	$ $1380$

Extra paid on hire purchase

\displaystyle \text{HP price} - \text{cash price}

e.g.

\displaystyle 1380 - 1200

\displaystyle = 180

Monthly instalment: interest on the loan for the whole time, then share it out

\displaystyle \dfrac{\text{loan} + \text{interest}}{\text{number of months}}

e.g.

\displaystyle \dfrac{900 + 180}{30}

\displaystyle = 36

$8\%$ per annum for $30$ months ( $2.5$ years): $\dfrac{900 \times 8 \times 2.5}{100}$ , so $180 interest

Interest as a percentage of the loan

\displaystyle \dfrac{\text{interest}}{\text{loan}} \times 100\%

e.g.

\displaystyle \dfrac{180}{900} \times 100

\displaystyle = 20

$20\%$ of the loan

📖 Worked example

The table shows the terms for buying a home theatre system on hire purchase. Find how much more the home theatre system costs on hire purchase than for cash.

Hire purchase	Home theatre system
Cash price	$1,200
Deposit	25% of the cash price
Monthly instalments	30 instalments of $36

Step 1 of 4

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 1200

\phantom{\text{Deposit}} = 300

📖 Worked example

Hui Min buys a sofa set on the hire-purchase terms in the table. The balance after the deposit is charged simple interest for the 18 months, and the balance plus the interest is paid back in 18 equal monthly instalments. Find each monthly instalment.

Hire purchase	Sofa set
Cash price	$960
Deposit	10% of the cash price
Interest on the balance	5% per annum, simple interest
Repayment	18 equal monthly instalments

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{10}{100} \times 960

\phantom{\text{Deposit}} = 96

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Sec 2 · G1 (N(T))

Money matters

Practise money matters with step-by-step help. Free account.

Start free

1. Simple interest

Symbol	Meaning	Example
$P$	principal: the amount deposited or borrowed	$ $2000$
$R$	rate, in % per year (per annum)	$3$
$T$	time, in years	$4$
$I$	interest	$ $240$

Simple interest

\displaystyle I = \dfrac{PRT}{100}

e.g.

\displaystyle I = \dfrac{2000 \times 3 \times 4}{100}

\displaystyle I = 240

Total amount: principal + interest

\displaystyle A = P + I

e.g.

\displaystyle A = 2000 + 240

\displaystyle A = 2240

Time in months: change to years first

\displaystyle T = \dfrac{\text{months}}{12}

e.g.

\displaystyle T = \dfrac{18}{12}

\displaystyle T = 1.5

📖 Worked example

Chen Wei puts $1,000 in a fixed deposit account that pays 1.5% per annum simple interest. Find the total amount in the account after 4 years.

Step 1 of 2

Substitute P, R and T into the formula

I = \dfrac{PRT}{100}

I = \dfrac{1000 \times 1.5 \times 4}{100}

= 60

📖 Worked example

Mei Ling deposits some money in a bank that pays simple interest of 2% per annum. After 5 years, the interest earned is $100. Find the amount of money Mei Ling deposited.

Step 1 of 2

Put the numbers you know into the formula

I = \dfrac{PRT}{100}

100 = \dfrac{P \times 2 \times 5}{100}

Practise this →

2. GST, service charge and discounts

Charge	Multiply by	Example
$10\%$ service charge	$1.10$	$50 \times 1.10$ , so $ $55$
$9\%$ GST	$1.09$	$55 \times 1.09$ , so $ $59.95$
$15\%$ discount	$0.85$	$80 \times 0.85$ , so $ $68$

Restaurant bill: service charge first, then GST on that total

\displaystyle 50 \times 1.10 \times 1.09

e.g.

\displaystyle 50 \times 1.10 \times 1.09

\displaystyle = 59.95

Discount first, then GST

\displaystyle 80 \times 0.85 \times 1.09

e.g.

\displaystyle 80 \times 0.85 \times 1.09

\displaystyle = 74.12

Price before GST: the price with GST is 109%

\displaystyle 109\% \to 218

e.g.

\displaystyle \dfrac{218}{109} \times 100

\displaystyle = 200

the price before GST is $200

📖 Worked example

Item	Price
Fried rice	$8.50
Iced lemon tea	$3.20
Chilli crab	$48.00

Step 1 of 3

Add up the bill (in dollars)

8.50 + 3.20 + 48.00 = 59.70

📖 Worked example

The price of an air-conditioner, including 9% GST, is $446.90. Find its price before GST.

Step 1 of 3

The price with GST is what percentage of the price before GST? (in dollars)

100\% + 9\% = 109\%

109\% \rightarrow 446.90

📖 Worked example

Item	Price
Chicken rice	$7.60
Tom yum soup	$11.80
Roti prata set	$6.60

Step 1 of 4

Add up the food (in dollars)

7.60 + 11.80 + 6.60 = 26

Practise this →

3. Utilities and bills

Bill	Charged for	How
electricity	kWh used	current reading $-$ previous reading, $\times$ the rate
water	m³ used, in tiers	the first part at the lower rate, the rest at the higher rate
mobile phone	minutes over the free time	monthly fee $+$ extra minutes $\times$ the rate

Electricity: units used

\displaystyle 24805 - 24315

e.g.

\displaystyle 24805 - 24315

\displaystyle = 490

at $27.5$ cents per kWh: $490 \times 27.5$ is $13\,475$ cents, which is $134.75

Water: 45 m³, the first 30 m³ at $1.20, the rest at $1.60

\displaystyle 30 \times 1.20 + 15 \times 1.60

e.g.

\displaystyle 30 \times 1.20 + 15 \times 1.60

\displaystyle = 60

📖 Worked example

The table shows a household's electricity meter readings for a month and the rate charged. Find the cost of the electricity used, in dollars.

Previous meter reading	Current meter reading	Rate
12460 kWh	12828 kWh	30 cents per kWh

Step 1 of 3

Units used = current reading − previous reading

12828 - 12460 = 368 \text{ kWh}

📖 Worked example

Mei Ling's mobile phone plan is shown in the table. In March, Mei Ling made 380 minutes of calls. Find the amount of Mei Ling's bill for March.

Monthly fee	Free talk time	Extra calls
$20	300 min	10 cents per min

Step 1 of 3

Extra minutes = minutes used − free minutes

380 - 300 = 80 \text{ min}

Practise this →

4. Currency exchange

Rate	S$ to the foreign currency	Back to S$
S$1 buys ¥108	multiply by $108$	divide by $108$
1 ringgit costs S$0.30	divide by $0.30$	multiply by $0.30$

S$200 into yen

\displaystyle 200 \times 108

e.g.

\displaystyle 200 \times 108

\displaystyle = 21600

¥ $21\,600$

¥16 956 back into Singapore dollars

\displaystyle \dfrac{16956}{108}

e.g.

\displaystyle \dfrac{16956}{108}

\displaystyle = 157

S$157

📖 Worked example

Currency	S$1 buys
Malaysian ringgit (RM)	3.4
Japanese yen (¥)	108
Australian dollars (A$)	1.2

Step 1 of 1

Use the exchange rate: multiply or divide?

800 \times 3.4

= 2720

Devi receives RM 2720.

📖 Worked example

Siti wants to change S$1000 into Malaysian ringgit. The rates at two money changers are shown in the table. Which money changer gives Siti more Malaysian ringgit?

Money changer	Rate
A	S$1 = RM 3.4
B	S$100 = RM 346.8

Step 1 of 3

Money changer A: the amount of Malaysian ringgit received

\text{A: } 1000 \times 3.4 = 3400

Practise this →

5. Instalments and hire purchase

Term	Meaning	Example
cash price	the price paid all at once	$ $1200$
deposit	paid at the start	$25\%$ of $1200$ : $ $300$
loan (balance)	cash price $-$ deposit	$ $900$
instalments	equal monthly payments	$30 \times 36$ : $ $1080$
hire-purchase price	deposit $+$ all the instalments	$ $1380$

Extra paid on hire purchase

\displaystyle \text{HP price} - \text{cash price}

e.g.

\displaystyle 1380 - 1200

\displaystyle = 180

Monthly instalment: interest on the loan for the whole time, then share it out

\displaystyle \dfrac{\text{loan} + \text{interest}}{\text{number of months}}

e.g.

\displaystyle \dfrac{900 + 180}{30}

\displaystyle = 36

$8\%$ per annum for $30$ months ( $2.5$ years): $\dfrac{900 \times 8 \times 2.5}{100}$ , so $180 interest

Interest as a percentage of the loan

\displaystyle \dfrac{\text{interest}}{\text{loan}} \times 100\%

e.g.

\displaystyle \dfrac{180}{900} \times 100

\displaystyle = 20

$20\%$ of the loan

📖 Worked example

The table shows the terms for buying a home theatre system on hire purchase. Find how much more the home theatre system costs on hire purchase than for cash.

Hire purchase	Home theatre system
Cash price	$1,200
Deposit	25% of the cash price
Monthly instalments	30 instalments of $36

Step 1 of 4

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 1200

\phantom{\text{Deposit}} = 300

📖 Worked example

Hire purchase	Sofa set
Cash price	$960
Deposit	10% of the cash price
Interest on the balance	5% per annum, simple interest
Repayment	18 equal monthly instalments

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{10}{100} \times 960

\phantom{\text{Deposit}} = 96

Practise this →

Practise money matters with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

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