Simple Vs Compound Interest
Calculate the simple interest on $4,000 at 6% for 2 years.
I=4000×0.06×2=480
Find the value of a $20,000 car after 1 year at 10% depreciation.
$18,000
What is the taxable income if gross income is $70,000 and deductions are $5,000?
$65,000
Find total repayment on $5,000 at 6% for 2 years.
5000(1.06)2=5618
Add GST to $300
$330
What does GST stand for?
Goods and Services Tax.
Find the compound total for $4,000 at 6% for 2 years.
A=4000(1.06)2=4494.40
Find the value after 2 years at 10%.
20000(0.9)2=16200
Calculate tax on $35,000.
35000−18200=16800
16800×0.19=319216800 × 0.19 = 319216800×0.19=3192
What is the interest paid on a repayment of $5,000 at 6% for 2 years
$618
Remove GST from $880
$800
How much is GST in Australia?
10%
How much more does compound interest earn than simple interest on $5,000 at 5% over 3 years?
Simple: 5000×0.05×3=7505000 × 0.05 × 3 = 7505000×0.05×3=750 → Total = 5750
Compound: 5000(1.05)3=5788.135000(1.05)^3 = 5788.135000(1.05)3=5788.13
Difference = $38.13
How much value is lost after 3 years at 10% from $20,000?
20000(0.9)3=14580
Loss = $5,420
Calculate tax on $60,000.
Excess over 45,000 = 15,000
15000×0.325=487515000 × 0.325 = 487515000×0.325=4875
Tax = 5092 + 4875 = 9967
Find total repayment on $15,000 at 8% for 3 years.
15000(1.08)3=18895.68
A person earns $750 per week and spends $680.
Find savings.
$70 surplus
What is the tax-free threshold in Australia (the amount you can earn before paying income tax)?
$18,200.
A person invests $8,000 for 4 years.
Option A: 5% simple
Option B: 4% compound
Which option earns more?
Simple: 8000×0.05×4=16008000 × 0.05 × 4 = 16008000×0.05×4=1600 → 9600
Compound: 8000(1.04)4=9369.868000(1.04)^4 = 9369.868000(1.04)4=9369.86
Simple earns more.
A car loses 20% in the first year and 20% again in the second year.
Is the total loss 40%? Explain with calculations.
Year 1: 100% → 80%
Year 2: 80% × 0.8 = 64%
Total loss = 36%, not 40%.
A person earns $80,000 and claims $10,000 in deductions.
Find:
a) Taxable income
b) Tax payable
c) Net income
Taxable = 70,000
Excess over 45,000 = 25,000
25000×0.325=812525000 × 0.325 = 812525000×0.325=8125
Tax = 5092 + 8125 = 13,217
Net = 56,783
Compare loans:
$20,000 at 5% for 4 years
$20,000 at 7% for 4 years
Which costs more?
5% → 24310.13
7% → 26215.21
7% costs more.
A $1,200 phone includes GST.
Find the GST amount only.
1200÷1.10=1090.91
GST = 109.09
What is the term used to describe money that earns “interest on interest”?
Compound interest.
At what interest rate would $10,000 earn $2,000 simple interest in 5 years?
2000=10000×r×5
2000=50000r2000 = 50000r2000=50000r
r=0.04=4%r = 0.04 = 4\%r=0.04=4%
After 3 years at 15% depreciation, a car is worth $12,282.
What was its original value?
A=P(0.85)3
12282÷0.614125=2000012282 ÷ 0.614125 = 2000012282÷0.614125=20000
Original value = $20,000
How much extra tax does someone earning $50,000 pay compared to someone earning $45,000?
Extra income = 5000
5000×0.325=16255000 × 0.325 = 16255000×0.325=1625
How much extra is paid on the 7% loan compared to the 5% loan?
Difference ≈ $1,905
A person invests $10,000 at 5% compound for 5 years.
They also take a $10,000 loan at 5% compound for 5 years.
Which grows faster — savings or debt?
They grow at the same rate mathematically.
If inflation is higher than the interest rate on your savings, does your money effectively gain or lose value over time?
It loses value.
Over 10 years, which grows more:
$6,000 at 4% compound or $6,000 at 6% simple?
Simple: 6000×0.06×10=36006000 × 0.06 × 10 = 36006000×0.06×10=3600 → 9600
Compound: 6000(1.04)10=8881.476000(1.04)^{10} = 8881.476000(1.04)10=8881.47
Simple earns more.
Explain why higher depreciation rates have a bigger long-term impact than they first appear.
Because depreciation is applied to the reduced value each year, compounding the loss.
Explain why someone earning $100,000 does NOT pay 32.5% of the full $100,000.
Only income above $45,000 is taxed at 32.5%. Lower portions are taxed at lower rates.
Explain how both interest rate and time affect total repayment.
Higher rates increase growth per year.
Longer time allows interest to compound more times.
Explain why saving early in life gives a financial advantage.
More time allows compound interest to grow significantly.
Why is compound interest sometimes called the “eighth wonder of the world”?
Because small amounts grow dramatically over long periods of time.