Simple Interest

Statement

For simple interest calculations:

\[ I = \frac{Prt}{100}, \quad A = P+I \]

where \(P\) is the principal, \(r\) is the annual rate of interest (%), \(t\) is the time in years, \(I\) is interest, and \(A\) is the final amount.

Why it’s true

• Simple interest grows linearly — the same amount is added each year.
• For one year: interest = \(P \times r/100\).
• For \(t\) years: interest = \(P \times r/100 \times t\).
• Total = principal + interest.

Recipe (how to use it)

1. Identify \(P\), \(r\), and \(t\).
2. Calculate \(I=(Prt)/100\).
3. Add to principal for total \(A=P+I\).

Spotting it

Look for problems with fixed yearly percentages, e.g. “£500 at 6% simple interest for 3 years”.

Common pairings

• Bank savings questions.
• Loans and repayments.
• Comparisons with compound interest.

Mini examples

1. £500 at 6% for 3 years → \(I=(500×6×3)/100=90\), \(A=590\).
2. £2000 at 4% for 5 years → \(I=(2000×4×5)/100=400\), \(A=2400\).
3. £800 at 10% for 2 years → \(I=(800×10×2)/100=160\), \(A=960\).

Pitfalls

• Forgetting to divide by 100 when rate is a percentage.
• Using compound instead of simple interest formula.
• Confusing years with months (convert months into years).

Exam strategy

• Write down values of \(P,r,t\) before calculating.
• Always check if question asks for interest or total amount.
• If given monthly/quarterly, convert time into years correctly.

Summary

Simple interest: \(I=(Prt)/100\), \(A=P+I\). Interest increases in a straight line with time.