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Number - Simple and Compound Interest

Grade 10IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Principal (P): The initial amount of money borrowed or invested.

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Rate (r): The percentage of the principal charged or earned as interest per period (usually per annum).

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Time (t or n): The duration for which the money is invested or borrowed, usually measured in years.

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Simple Interest: Interest calculated only on the original principal amount throughout the entire period.

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Compound Interest: Interest calculated on the principal plus any accumulated interest from previous periods.

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Depreciation: The decrease in value of an asset over time, calculated using the compound interest formula with a negative rate.

📐Formulae

Simple Interest: I=P×R×T100I = \frac{P \times R \times T}{100}

Total Amount (Simple Interest): A=P+IA = P + I

Total Amount (Compound Interest): A=P(1+r100)nA = P(1 + \frac{r}{100})^n

Compound Interest Only: CI=A−PCI = A - P

Depreciation (Value after n years): V=P(1−r100)nV = P(1 - \frac{r}{100})^n

💡Examples

Problem 1:

Calculate the simple interest earned on $5,000 invested at a rate of 4% per annum for 3 years.

Solution:

I=5000×4×3100=600I = \frac{5000 \times 4 \times 3}{100} = 600

Explanation:

Substitute the values into the Simple Interest formula: P=5000P=5000, R=4R=4, and T=3T=3. The total interest earned is $600.

Problem 2:

A bank offers a compound interest rate of 5% per year. If $2,000 is deposited for 2 years, calculate the total amount in the account at the end of the term.

Solution:

A=2000(1+5100)2=2000(1.05)2=2000(1.1025)=2205A = 2000(1 + \frac{5}{100})^2 = 2000(1.05)^2 = 2000(1.1025) = 2205

Explanation:

Use the compound interest formula A=P(1+r/100)nA = P(1 + r/100)^n. Here P=2000P=2000, r=5r=5, and n=2n=2. The result $2,205 is the principal plus the interest compounded annually.

Problem 3:

A car is bought for $15,000. It depreciates in value by 12% each year. Calculate the value of the car after 3 years, giving your answer to the nearest dollar.

Solution:

V=15000(1−12100)3=15000(0.88)3≈10222.08V = 15000(1 - \frac{12}{100})^3 = 15000(0.88)^3 \approx 10222.08

Explanation:

Apply the depreciation formula where the rate is subtracted from 1. P=15000P=15000, r=12r=12, and n=3n=3. Calculating 15000×0.68147215000 \times 0.681472 gives 10,222.08.Roundedtothenearestdollar,thevalueis10,222.08. Rounded to the nearest dollar, the value is 10,222.