Simple Interest
- Simple Interest – Definition
- Simple Interest Formula
- Calculating Simple Interest – Step-by-Step Process
- Finding Simple Interest – Practice
- Problem Solving with Simple Interest
- Solving for Principal ($P$)
- Solving for Time ($t$)
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Learning text on the topic Simple Interest
Simple Interest – Definition
When we talk about money, whether it's saving in a bank, borrowing for a car, or investing, interest often comes into play. Simple interest is a way to calculate the extra money earned or paid on a certain amount of money, called the principal, over a period of time. It's like a fee you pay for using someone's money or a reward for saving.
Simple interest is calculated using the formula $I = P \times r \times t$, where I is the interest, P is the principal amount, r is the annual interest rate as a decimal, and t is the time. Understanding simple interest is crucial as it helps you calculate how much extra money you'll earn or need to pay on investments or loans, making financial planning clearer and more straightforward.
Simple Interest Formula
The formula used to calculate simple interest is the product of the principal amount, interest rate, and time. These three pieces of information must be known to find the simple interest.
Take a look at the meaning of each of these variables in the formula.
| Symbol | Meaning | Example |
|---|---|---|
| I | Interest earned or paid | - |
| P | Principal amount (initial money) | £200 |
| r | Annual interest rate (in decimal form) | 0.05 (5% ÷ 100) |
| t | Time the money is invested or borrowed (years) | 3 years |
Conversion of Percent to Decimal: To convert an interest rate from a percent to a decimal, divide by 100. For example, 5% becomes 0.05.
Understanding how to and being fluent in converting between percent, fractions and decimals is a skill that will help calculate simple interest. Have a look at our text on fractions and percentages.
Calculating Simple Interest – Step-by-Step Process
| Step | Action | Description |
|---|---|---|
| 1 | Identify Principal Amount (P) | Identify the principal amount (P), which is the initial amount of money. |
| 2 | Convert Rate to Decimal | Convert the interest rate from a percentage to a decimal by dividing by 100. |
| 3 | Determine Time Period (t) | Determine the time period (t) in years for which the interest will be calculated. |
| 4 | Use Simple Interest Formula | Use the simple interest formula $I = P \times r \times t$ to calculate the interest. |
| 5 | Calculate Total Amount | Calculate the total amount after interest by adding the principal amount and the interest earned. |
Finding Simple Interest – Practice
Practise finding the simple interest on your own.
Problem Solving with Simple Interest
The formula for calculating interest can also be used to problem-solve and work backwards to find missing values, such as the principal, rate or time.
Solving for Principal ($P$)
Given:
- Interest ($I$) = £150
- Interest rate ($r$) = 5% per year or 0.05 in decimal
- Time ($t$) = 3 years
We want to find the principal amount ($P$).
Rearrange the formula to solve for $P$: $P = \frac{I}{r \times t}$
Substitute in the values: $P = \frac{150}{0.05 \times 3} = \frac{150}{0.15} = 1000$
Answer: The principal amount is £1000.
Solving for Time ($t$)
Given:
- Interest ($I$) = £200
- Principal amount ($P$) = £1000
- Interest rate ($r$) = 4% per year or 0.04 in decimal
We want to find the time ($t$).
Rearrange the formula to solve for $t$: $t = \frac{I}{P \times r}$
Substitute in the values: $t = \frac{200}{1000 \times 0.04} = \frac{200}{40} = 5$
Answer: The time is 5 years.
Now try more worded problems with various unknowns:
Simple Interest – Summary
Key Learnings from this text:
- Simple interest is a straightforward way to calculate interest on a principal amount over time.
- The formula for simple interest is $\bf{I = P r t}$.
- The formula is also useful for finding missing information when the interest amount is already known.
- Always convert the interest rate from a percentage to a decimal before using the formula.
- The total amount after the interest period is the sum of the principal and the interest earned.
Simple Interest – Frequently Asked Questions
Simple Interest exercise
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Understand the formula to find simple interest.
HintsThe formula for simple interest is calculated by multiplying the principal amount (the original amount of money) by the interest rate (the percentage charged or earned) and the time (how long the money is borrowed or invested).
The formula is expressed as:
Simple Interest = Principal × Rate ($r$) × Time ($t$)
For example, if you invest £100 (principal) at an interest rate of 5% per year for 3 years, the simple interest earned would be calculated as follows:
Simple Interest = £100 × 5% × 3 = £100 × 0.05 × 3 = £15
So, you would earn £15 in interest over 3 years.
Solution- Interest: The amount of money earned or paid for borrowing or lending money, calculated based on the principal, interest rate, and time.
- Principal: The original amount of money borrowed or invested.
- Rate: The percentage of the principal that is paid as interest per period.
- Time: The duration for which the money is borrowed or invested, typically in years.
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Analyse the information in each problem to find the interest.
Hints$I$ = Interest: The amount of money earned or paid for borrowing or lending money, calculated based on the principal, interest rate and time.
$P$ = Principal: The original amount of money borrowed or invested.
$r$ = Rate: The percentage of the principal that is paid as interest per period. This value is always given as a percent.
$t$ = Time: The duration for which the money is borrowed or invested. This value is typically presented in years.
Solution1.) Principal = £500 Rate = 2% per year Time = 3 years
2.) Principal = £10 Rate = 1% per month Time = 6 months
3.) Principal = £15,500 Rate = 5% per year Time = 4 years
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Calculate the simple interest.
HintsThe formula to find the simple interest is seen here.
- $I$ = Interest: The amount of money earned or paid for borrowing or lending money, calculated based on the principal, interest rate and time.
- $P$ = Principal: The original amount of money borrowed or invested.
- $r$ = Interest Rate: The percentage of the principal that is paid as interest per period.
- $t$ = Time: The duration for which the money is borrowed or invested, typically in years.
The rate needs to be converted into a decimal.
To change a percent to decimal, divide by 100.
$2\%$ = $\frac{2}{100}$ = $0.02$
SolutionThe formula used is $I=Prt$
$P = 500$
$r = 2% = 0.02$
$t = 3$ years
The solution is:
$I = \bf{(500)(0.02)(3)}$
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Understand the process to finding the simple interest of a real-world situation.
HintsTo change a percent to a decimal, divide the percent value by 100. Essentially, you are moving the decimal point two places to the left. For example, to convert $75\%$ to a decimal, divide $75$ by $100$, which equals $0.75$.
- $I$ = Interest: The amount of money earned or paid for borrowing or lending money, calculated based on the principal, interest rate and time.
- $P$ = Principal: The original amount of money borrowed or invested.
- $r$ = Interest Rate: The percentage of the principal that is paid as interest per period.
- $t$ = Time: The duration for which the money is borrowed or invested, typically in years.
SolutionAri borrows £1,500 from a friend who charges them a simple interest of 4% per year. If Ari takes 2 years to pay back the loan, how much interest will they pay?
The formula used to find the interest is $\bf{I=Prt}$.
The principal amount that is borrowed is £1,500, the interest rate written as a decimal is $\bf{0.04}$, and the time period is 2 years.
When these values are substituted into the formula, the equation is $\bf{I=(1,500)(0.04)(2)}$.
After calculating, Ari will have accrued £120 in interest on top of the £1,500 they already owe back to their friend.
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What is the formula to calculate simple interest?
HintsSimple interest is a way of calculating the interest you earn or pay on a loan or investment based on the original amount (principal), the interest rate and the time the money is borrowed or invested.
The formula for simple interest is calculated by multiplying the original amount of money ($P$) by the percentage charged or earned ($r$) and then how many years the money is borrowed or invested ($t$).
Solution$I$ = Interest: The amount of money earned or paid for borrowing or lending money, calculated based on the principal, interest rate and time.
$P$ = Principal: The original amount of money borrowed or invested.
$r$ = Rate: The percentage of the principal that is paid as interest per period.
$t$ = Time: The duration for which the money is borrowed or invested, typically in years.
-
Calculate the simple interest.
HintsUse the formula, $I=Prt$.
- $I$ = Interest: The money earned or paid from borrowing or lending, based on principal, rate and time.
- $P$ = Principal: The initial amount borrowed or invested.
- $r$ = Rate: The percent of principal paid as interest per period.
- $t$ = Time: How long the money is borrowed or invested, usually in years.
SolutionTo find the interest earned, use the formula $I=Prt$.
$I=(3,000)(0.025)(3)$
$I$ = £225
