Simple Interest (Grade 10 NSC Matric Mathematics): Revision Notes
Simple Interest
What is interest?
When you put money in a bank account or borrow money from someone, interest becomes involved. Think of interest as the "cost of money" - it's what you earn when you lend money, or what you pay when you borrow money.
Interest is the money charged for borrowing money, usually expressed as a percentage of the borrowed amount.
For example, if you deposit R 1000 into a bank account, you're essentially lending that money to the bank. In return, the bank pays you interest. Similarly, if you borrow money from the bank, you'll pay interest on that loan.
Understanding simple interest
Simple interest is interest calculated only on the initial amount that you invested or borrowed. This initial amount is called the principal.
Simple interest is different from compound interest because it doesn't include interest earned on previous interest payments. It only considers the original amount throughout the entire period.
Key terms you need to know
- Principal (P): The initial amount of money invested or borrowed
- Accumulated amount (A): The final total amount after interest has been added
- Interest rate (i): The percentage rate expressed as a decimal (e.g., 5% = 0.05)
- Number of years (n): The time period for the investment or loan
- Per annum (p.a.): This means "per year"
The simple interest formula
The Simple Interest Formula
The formula for calculating simple interest problems is:
Where:
- A = accumulated amount (final amount)
- P = principal amount (initial amount)
- i = interest rate written as a decimal
- n = number of years
How the formula works
Let's break this down with a simple example. If you invest R 1000 at 5% simple interest for 1 year:
The interest earned = R 1000 × 5% = R 1000 × 0.05 = R 50
Your final amount = Initial amount + Interest = R 1000 + R 50 = R 1050
Using the formula: ✓
Worked examples
Worked Example 1: Calculating the final amount on a deposit
Question: Carine deposits R 1000 into a bank account that pays 7% p.a. simple interest for 3 years. How much will be in her account at the end?
Solution:
Step 1: Write down the known values
- P = 1000
- i = 0.07 (7% as a decimal)
- n = 3
Step 2: Write down the formula
Step 3: Substitute the values
Step 4: Write the final answer
- At the end of 3 years, Carine will have R 1210 in her bank account.
Worked Example 2: Calculating the amount to repay on a loan
Question: Sarah borrows R 5000 at 12.5% p.a. simple interest for 2 years. How much must she repay?
Solution:
Step 1: Write down the known values
- P = 5000
- i = 0.125 (12.5% as a decimal)
- n = 2
Step 2: Write down the formula
Step 3: Substitute the values
Step 4: Write the final answer
- Sarah will need to repay R 6250 to her neighbour.
Worked Example 3: Finding the time period needed
Question: Prashant deposits R 30 000 at 7.5% p.a. simple interest. How long must he invest to reach R 45 000?
Solution:
Step 1: Write down the known values
- A = 45 000
- P = 30 000
- i = 0.075
Step 2: Write down the formula
Step 3: Substitute and solve for n
Step 4: Convert to years and months
- 6.67 years = 6 years and 8 months
Prashant must invest for 6 years and 8 months to reach his goal.
Worked Example 4: Finding the required interest rate
Question: At what simple interest rate should Fritha invest R 2500 to grow to R 4000 in 5 years?
Solution:
Step 1: Write down the known values
- A = 4000
- P = 2500
- n = 5
Step 2: Write down the formula
Step 3: Substitute and solve for i
Step 4: Convert to percentage
- i = 0.12 = 12% p.a.
Fritha needs a simple interest rate of 12% p.a.
Exam Tips and Common Mistakes
- Always convert percentages to decimals when using the formula (divide by 100)
- Use your calculator efficiently - do all calculations in one go to avoid rounding errors
- Check your units - make sure you're working in years, not months
- Read carefully - distinguish between "interest earned" and "total amount"
- Show all working - write down known values, formula, substitution, and final answer
- Don't forget units - always include "R" for currency and specify time periods
Rearranging the formula
You can rearrange the simple interest formula to find any missing variable:
Formula Variations
- To find P:
- To find i:
- To find n:
These rearranged formulas are useful when you need to find the principal, interest rate, or time period instead of the accumulated amount.
Key Points to Remember:
- Simple interest only calculates interest on the original principal amount
- The formula is A = P(1 + in) where all variables must be in consistent units
- Always convert percentages to decimals before substituting into the formula
- Show your working step-by-step - list known values, write the formula, substitute, then give your final answer
- Use your calculator wisely - do calculations in one go to minimise rounding errors