Find the simple interest rate per cent per annum if $4,000 grows to $5,000 in 5 years.

To find the simple interest rate, we start by using the formula for simple interest:

\[
A = P(1 + rt)
\]

where:
- $ A $ is the final amount, 
- $ P $ is the principal amount, 
- $ r $ is the rate of interest per annum, and 
- $ t $ is the time in years.

Given:
- $ P = 4000 $ (the initial amount),
- $ A = 5000 $ (the final amount),
- $ t = 5 $ years.

We need to find the interest rate $ r $.

Rearranging the formula to solve for $ r $:

\[
r = \frac{A - P}{Pt}
\]

Substitute the given values:

\[
r = \frac{5000 - 4000}{4000 \times 5}
\]

Let's calculate the value of $ r $.The simple interest rate is **5% per annum**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How is compound interest different from simple interest?
2. What would be the final amount if the interest rate was 7% per annum instead?
3. How can you calculate the interest rate if the final amount and time are known?
4. What formula would you use to find the principal amount if the rate and time are given?
5. How does increasing the time period affect the total interest earned?

**Tip:** Always remember to convert the interest rate to a percentage by multiplying by 100.

Learn how to calculate the simple interest rate when $4,000 grows to $5,000 in 5 years using the simple interest formula. This step-by-step solution is ideal for students in Grades 6-8 and covers essential concepts such as rate of interest and linear equations.

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