Percent Problems involving Simple Interest

Simple Interest Word Problems
Simple interest word problems involve calculations related to loans or investments where the interest earned or paid is a fixed percentage of the principal amount over a specific period. The key difference between simple interest and compound interest is that simple interest is only calculated on the initial principal, whereas compound interest is calculated on the principal and any accumulated interest.

What is the Simple Interest Formula?
The formula for calculating simple interest is:
Simple Interest = principal × rate × time
I = P × r × t
Where:
I = Simple Interest (the amount of interest earned or paid)
P = Principal (the initial amount of money borrowed or invested)
R = Annual Interest Rate (expressed as a decimal)
T = Time (the duration of the loan or investment in years)

Sometimes, you might need to find the total amount (A) after the interest has been added to the principal:
A = P + I
or
A = P(1 + RT)

The following diagrams show the Simple Interest Formula and how the formula can be transformed to solve for each variable. Scroll down the page for more examples and solutions on how to use the Simple Interest Formula.

 

Here are some common types of interest word problems:

1. Finding the Simple Interest:
   Problem: You deposit $1000 in a savings account that earns simple interest at an annual rate of 5% for 3 years. How much interest will you earn?
   Solution:
   \(P = $1000\)
   \(R = 5% = 0.05\)
   \(T = 3\) years
   \(I = P \times R \times T = 1000 \times 0.05 \times 3 = $150\)
   

You will earn $150 in simple interest.

2. Finding the Total Amount:
   Problem: If you borrow $5000 at a simple interest rate of 8% per year for 2 years, what is the total amount you will have to repay?
   Solution:
   \(P = $5000\)
   \(R = 8% = 0.08\)
   \(T = 2\) years
   \(I = P \times R \times T = 5000 \times 0.08 \times 2 = $800\)
   \(A = P + I = 5000 + 800 = $5800\)
   

The total amount to repay is $5800.

3. Finding the Interest Rate:
   Problem: You invested $2000 for 5 years and earned RM600 in simple interest. What was the annual interest rate?
   Solution:
   \(I = $600\)
   \(P = $2000\)
   \(T = 5\) years
   Using \(I = P \times R \times T\), we can solve for \(R\):
   \(R = \frac{I}{P \times T} = \frac{600}{2000 \times 5} = \frac{600}{10000} = 0.06\)
   

The annual interest rate was \(0.06 \times 100% = 6%\).

4. Finding the Time Period:
   Problem: You invested $3000 at a simple interest rate of 4% per year. How many years will it take for your investment to earn $360 in interest?
   Solution:
   \(I = $360\)
   \(P = $3000\)
   \(R = 4% = 0.04\)
   Using \(I = P \times R \times T\), we can solve for \(T\):
   \(T = \frac{I}{P \times R} = \frac{360}{3000 \times 0.04} = \frac{360}{120} = 3\)
   

It will take 3 years to earn $360 in interest.

5. Problems Involving Months or Days:
   When the time period is given in months or days, you need to convert it to years before using the formula:
   Months to Years: Divide the number of months by 12.
   Days to Years: Divide the number of days by 365 (assuming a non-leap year).
   Problem: You borrow $1200 at a simple interest rate of 6% per year for 9 months. How much interest will you owe?
   Solution:
   \(P = $1200\)
   \(R = 6% = 0.06\)
   \(T = \frac{9}{12} = 0.75\) years
   \(I = P \times R \times T = 1200 \times 0.06 \times 0.75 = $54\)
   

You will owe $54 in interest.

Simple Interest Word Problems
This video shows how to solve for a missing part of the interest formula when the interest is given by substituting known values and solving for the unknown variable.

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Simple Interest I = prt
This video lesson shows how to calculate Simple Interest using this equation I = prt. It also shows how to manipulate that equation to solve for all 4 variables.

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