GCSE Maths

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Rounding to the Nearest 10, 100, 1000, and Beyond
Significant Figures
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Simple Interest
Rounding and Estimation
Standard Form
Four Operational Rules
Conversion of Units to other Units
Compound Interest
Surds
Rational and Irrational Numbers
Greatest and Least Possible Values
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Algebra
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Algebraic Notation
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Collecting Like Terms
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Factorisation
Factorising Quadratic Expressions
Factorising Quadratics with a Coefficient of x Squared Greater than 1
The Quadratic Formula
The Difference of Two Squares
Subject of Formula
Solving Linear Equations
Quadratic Equations
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Sequences and Nth Term
Arithmetic and Geometric Sequences
Quadratic Sequences
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Ratio, Proportion and Rates of Change
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Ratios
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2D Shapes
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Probability
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Introduction to Probability
Relative Frequency
Sample Space
Probability of Single Events
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Probability Trees
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Set Notation
Venn diagrams
The Complement of a Set
Statistics
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Population and samples
Representing data
Vectors
Mensuration and Calculation
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Area
Volume
Congruence and similarity
Pythagoras’ theorem
Sine and cosine rule
Area of a triangle
Standard units of measure
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Simple Interest

GCSE Maths Numbers Simple Interest

Interest is either earned when we deposit money into a bank or paid when we borrow money. Simple interest is calculated using a straightforward formula that considers the principal amount, the interest rate, and the time for which the money is deposited or borrowed.

Formula for Simple Interest

The formula for simple interest is:

I = \frac{P \times R \times T}{100}

Where:

  • I = Simple interest earned or paid
  • P = Principal amount (money deposited or borrowed)
  • R = Rate of interest (as a percentage, e.g., 5%, 12%, etc.)
  • T = Time (in years)

Let’s look at some examples.

Examples

Example 1: Calculating the Final Amount after Interest

Mr White deposited £5000 into a bank for 5 years, earning 2% interest on his money per year. How much will he have in his account after the 5 years?

• P = Principal amount = £5000

• R = Rate of interest = 2\% = 0.02

• T = Time = 5 years

Interest: I=\frac{P \times R \times T}{100} = \frac{£5000 \times 2 \times 5}{100} = £500

The interest for 5 years is £500. So, at the end of 5 years, Mr White will have £5000 (principal) + £500 (interest) = £5500 (final amount).

Example 2: Calculating Interest and Total Amount Paid for a Loan

Bernard took a loan of £10,000 from his bank and will pay interest on this sum for 10 years at the rate of 5% per annum. Find how much interest he should pay after 10 years and the total amount he paid.

• P = £10,000

• R = 5%

• T = 10 years

Using I=\frac{P \times R \times T}{100} =\frac{£10,000 \times 5 \times 10}{100} = £5000

This is the interest Bernard will pay after 10 years. The total amount of money to be repaid is £10,000 (principal) + £5,000 (interest) = £15,000 (total amount paid).

Example 3: Finding the Amount Borrowed

A sum of money was borrowed from a bank at a 7.5% interest per year for 4 years. The interest amounted to £150. What is the amount borrowed?

Using I=\frac{P \times R \times T}{100} and P is unknown:

• 150 =\frac{P \times 7.5 \times 4}{100}

• 150 =\frac{30P}{100}

• 15,000=30P

• P = 500

The amount borrowed is £500.

Example 4: Finding the Interest Rate per Annum

£50,000 was paid to Mrs Mary after investing £40,000 for 6 years into a bank. Find the interest rate per annum.

Using I=\frac{P \times R \times T}{100} with I = £50,000 - £40,000 = £10,000 and T = 6 years, we have:

• 10,000 =\frac{40,000 \times R \times 6}{100}

• 10,000 =\frac{240,000R}{100}

• 10,000 = 2400R

• R =\frac{10,000}{2400} = 4.166...

• R = 4.2% (to one decimal place)

Example 5: Finding the Loan Duration

A sum of £4500 was borrowed from a firm paying 2.5% interest rate per annum. The interest paid was £750. Find how long the sum was loaned.

Using I=\frac{P \times R \times T}{100} with I = £750, P = £4500, and R = 2.5, we have:

• 750 =\frac{4500 \times 2.5 \times T}{100}

• 750 = 112.5T

• T =\frac{750}{112.5}

• T = 6\frac{2}{3} years

• T = 6 years, 8 months

Example 6: Calculating Interest Earned in a Specific Time Period

£500 is deposited into a bank paying a 3% interest rate per annum. How much interest is earned in 4 months?

Using I=\frac{P \times R \times T}{100} with P = £500, R = 3, and T=\frac{4}{12} (4 months is \frac{4}{12} of a year), gives:

• I=\frac{500 \times 3 \times \frac{4}{12}}{100}

• I = £5

The interest earned in 4 months is £5.

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