Financial Mathematics

​Financial Maths Revision

​Key topics:

​ Percentage of amounts;

Buying on terms i.e. deposits​

Mark ups and discounts;

Successive discounts;​

Simple Interest;

Compound Interest;

Depreciation.​

​Mark Ups and Discounts

A mark-up represents a percentage increase.

​

A discount represents a percentage decrease.​

​Therefore the hose reel now costs $156.

Multiple Choice

A jacket costs $80. In a sale, the value is discounted by 15%. How much is it now worth?

• $65

• $68

• $70

• $95

Multiple Choice

If you mark up an item costing $200 by 40%, how much is it now worth?

• $220

• $240

• $260

• $280

Multiple Choice

If you discount an item costing $1,800 by 19%, how much is it now worth?

• $342

• $1,458

• $1,781

• $2,142

Multiple Choice

If you mark up an item costing $125 by 15%, how much is it now worth?

• $138.50

• $140

• $143.75

• $150.25

​Percentage Change (Profit and Loss)

Profit and Loss can be found via the same formula. The only difference is one value goes up whereas the other goes down.

A ticket for the 'footy' used to cost $12. It now costs $18. Find the % change.

​Therefore, there has been a 50% increase in the cost of a ticket for the 'footy'.

Multiple Choice

A train ticket from Manchester to London cost $150 in 2012. In 2022, it costs $195. Calculate the percentage change?

• 20%

• 25%

• 30%

• 45%

Multiple Choice

A pair of jeans used to cost $230, they are discounted to $130. Calculate the percentage change? Round to the nearest whole number.

• 21%

• 36%

• 39%

• 43%

​Successive Discounts

Successive discounts mean two or more discounts are offered to the value of a product.​ There isn't a formula to use. The example below highlights the process.

Bunnings has an offer in store, everything is reduced by 25%. If you are a tradesperson, a further 5% is removed. How much would an item which usually costs $360? ​

​Therefore, the item would be reduced to a cost of $256.50. This would be a saving of $103.50​.

Multiple Choice

A pair of runners are priced at $200 at Rebel. An in-store reduction of 20% discount is offered followed by a 10% discount for all Rebel members. Find the cost of the runners after the two discounts have been applied.

• $140

• $144

• $156

• $170

Multiple Choice

Greyhound coaches are offering a 10% reduction on the price of all coach travel. If you are a senior citizen, a further 4% will be offered as a reduction. If a ticket from Melbourne to Sydney usually costs $80. Find the percentage change in the cost of the ticket under these new conditions.

• 13.2%

• 13.6%

• 14%

• 15%

​Simple Interest

Simple interest represents a linear increase or decrease in the value. For example, a bank increases the amount of money in your account by $300 per year. The amount is always the same and isn't affected year to year.​ The answer from the formula provides you with the interest.

​Alan invests $6,000 into a bank account paying 2.5% p.a., simple interest. How much will he have in his account after 3 years?

​This means he will earn $450 over the 3 years.

​

The amount in his bank account is therefore, $6,450.​

Multiple Choice

The Interest accrued: ?

Principal Invested: $4,000

Interest Rate: 3% p.a. simple interest

Time Period: 5 years 

• $500

• $600

• $700

• $4,600

Multiple Choice

The Interest accrued: ?

Principal Invested: $10,000

Interest Rate: 2.5% p.a. simple interest

Time Period: 6 years 

• $1,000

• $1,200

• $1,500

• $11,500

Multiple Choice

The Interest accrued: ?

Principal Invested: $42,000

Interest Rate: 1.5% p.a. simple interest

Time Period: 18 months 

• $945

• $1,000

• $11,340

• $53,430

Multiple Choice

The Interest accrued: ?

Principal Invested: $30,000

Interest Rate: 3.6% p.a. simple interest

Time Period: 30 months 

• $900

• $2,400

• $2,700

• $32,400

Multiple Choice

The Interest accrued: ?

Principal Invested: $25,000

Interest Rate: 1.85% p.a. simple interest

Time Period: 18 weeks 

• $8,325

• $120

• $140

• $160

Multiple Choice

The Interest accrued: $10,800

Principal Invested: ?

Interest Rate: 12% p.a. simple interest

Time Period: 3 years

• $20,000

• $30,000

• $40,000

• $50,000

Multiple Choice

Frank borrows $40,000 from the bank to buy a new car. The rate is 3.6% p.a. simple interest, the time frame to pay back the loan is 5 years. How much does Frank need to pay back in total?

• $7,200

• $30,500

• $47,200

• $50,000

Multiple Choice

Rhiannon borrows (steals) $1,200,000 from the bank to buy a new house. The rate is 2.5% p.a. simple interest, the time frame to pay back the loan is 30 years. How much does Rhiannon need to pay back in total?

• $1,200,000

• $2,100,000

• $3,000,000

• $4,200,000

​Compound Interest

Compound interest represents a non-linear increase or decrease in the value. For example, a bank increases the amount of money in your account by 2% per year. The answer from the formula provides you with the final amount (A).

​Alanah invests $6,000 into a bank account paying 2.5% p.a., compounding annually. How much will she have in her account after 3 years?

​Alanah will therefore have $6,461.34.

​

She will have accrued $461.34 in interest.​

​Compound Interest (Varying Periods)

Compound interest doesn't always work on an annual basis. Sometimes the investment will compound: daily, weekly, monthly, quarterly or semi-annually. When this happens, we adjust our formula.

​Alanah invests $6,000 into a bank account paying 2.5% p.a., compounding monthly. How much will she have in her account after 3 years?

​Alanah will therefore have $6,466.80.

​

She will have accrued $466.80 in interest.​

Multiple Choice

Alan invests $40,000 at a rate of 3.5% p.a., compounding annually for 6 years. Find the amount in his account at the end of this period (to the nearest dollar).

• $49,170

• $9,170

• $8,400

• $48,400

Multiple Choice

Beth invests $320,000 at a rate of 2.6% p.a., compounding annually for 3 years. Find the amount in her account at the end of this period (to the nearest dollar).

• $25,615

• $345,615

• $24,960

• $344,960

Multiple Choice

Deborah invests $60,000 at a rate of 12.45% p.a., compounding annually for 3 years. Find the amount of interest earned over the 3 year period.

• $82,410

• $22,410

• $25,316

• $85,316

Multiple Choice

Eric invests $32,000 at a rate of 2.4% p.a., compounding quarterly for 3 years. Find the amount in his account at the end of the 3 years.

• $2,300

• $26,540.24

• $36,893.49

• $34,381.57

Multiple Choice

Freya invests $12,000 at a rate of 6.2% p.a., compounding monthly for 5 years. Find the amount in her account at the end of the 5 years.

• $18,234.98

• $15,720

• $16,210.78

• $16,348.05

Multiple Choice

Henrietta invests $1,500 at a rate of 12.6% p.a., compounding daily for 25 days. Find the amount in his account at the end of the 25 days.

• $1,513

• $4,800

• $2,678

• $5,330

​Depreciation

Depreciation represents a non-linear decrease in the value. For example, a car reduces in value at a rate of 30% per year. The answer from the formula provides you with the final amount (A).

​Samantha buys a car for $40,000. Its value depreciates at a rate of 15% p.a., compounding quarterly. How much is it worth after 5 years?

​The car will be worth $16,624.08.

​

The car will have lost $21,375.92 in value.

Multiple Choice

Kevin buys a classic car and watches the value depreciate at a rate of 4% p.a., compounding quarterly. If he bought the car for $40,000. How much is it worth 2 years later?

• $36,909.79

• $36,736

• $40,000

• $43,314.27

Multiple Choice

Lin buys a laptop for $3,200. Its value plummets at a rate of 15% p.a., compounding annually. How much is it worth after 4 years?

• $1,280

• $1,920

• $4,870.42

• $1,670.42

Multiple Choice

Michael buys a laptop for $5,500. Its value plummets at a rate of 10% p.a., compounding monthly. How much is it worth after 7 years?

• $2,456.67

• $2,723.22

• $8,223.22

• $1,698.58

Multiple Choice

Nethuli buys a new fridge for $4,200. Its value plummets at a rate of 8.8% p.a., compounding daily. How much is it worth after 5 years?

• Worthless

• $2,704.81

• $2,352

• $1,896.65

Multiple Choice

Quentin invests $250,000 into the share market. He makes a bad decision and his investment depreciates at a rate of 90% p.a., compounding daily. He needs to get the money out asap but has to wait 30 days. How much remains after the 30 day period?

• the money will have all gone after the 30 days

• $5,761,166.13

• $232,153.08

• $283.414.67

​Buying on Terms

​Cameron wants to buy a new set of golf clubs with a retail price of $2,000. He puts down a 20% deposit and agrees to pay the rest of the balance in equal monthly instalments of $80 over a two year period. How much does he spend in total?

​Deposit: 20% of $2,000

​This means he puts down $400 to secure the golf clubs, he has a further $1,600 to pay.

​Conditions of the Loan:

​This means he pays $1,920 for the clubs, this is $320 more than he needed to pay. Hence he has paid $320 in interest.

​Cameron has spent a total of $2,320 on his golf clubs (deposit + the conditions)

Multiple Choice

A new refrigerator costs $1,600. The rate is 4.52% p.a. simple interest, the time frame to pay back the loan is 15 months. Phil puts down a 10% deposit and borrows the rest from the bank. How much does Phil pay for the refrigerator in total? (Round to the nearest dollar)

• $1,521

• $1,681

• $1,690

• $2,000

Multiple Choice

John's monthly repayments on his car are $126 a month over 5 years. Calculate his total repayments

• $720

• $982

• $7560

• $4570

Multiple Choice

Michael pays $35 per month for 5 years for a new fridge. How much did it cost in total?

• $175

• $1,500

• $2,100

• $3,400

Multiple Choice

Nicola buys a new car for $25,000. She pays an initial deposit of 10% and then monthly payments of $600 for the period of 4 years. How much did she pay extra in interest for her car?

• $6,300

• $31,300

• $3,800

• $10,000