What sum of money will amount to
₹6,400 in 4 years at a simple
interest rate of 5% per annum? 

To find the sum of money (principal \( P \)) that will amount to ₹6,400 in 4 years at a simple interest rate of 5% per annum, we can use the formula for simple interest:

\[
A = P + SI
\]

Where:
- \( A \) is the total amount after interest (₹6,400 in this case),
- \( P \) is the principal (the unknown value we want to find),
- \( SI \) is the simple interest,
- \( r \) is the interest rate (5% per annum),
- \( t \) is the time in years (4 years).

First, let's calculate the simple interest:

\[
SI = \frac{P \times r \times t}{100}
\]

Substitute the values for \( r \) and \( t \):

\[
SI = \frac{P \times 5 \times 4}{100} = \frac{20P}{100} = 0.2P
\]

Now, using the formula \( A = P + SI \):

\[
6400 = P + 0.2P
\]

This simplifies to:

\[
6400 = 1.2P
\]

Solving for \( P \):

\[
P = \frac{6400}{1.2} = 5333.33
\]

Therefore, the principal amount is ₹5,333.33.

### Would you like more details or further explanation on any part?

Here are some related questions for practice:
1. What would the interest be if the principal was ₹7,000 for the same conditions?
2. How would the result change if the interest rate was 6% instead of 5%?
3. What is the total interest earned in this case over 4 years?
4. How long would it take for ₹5,333.33 to amount to ₹7,000 at 5% simple interest?
5. How much would you need to invest to get ₹10,000 in 5 years at 5% simple interest?

#### Tip: In simple interest, the interest is directly proportional to time and rate, so small changes in either can have significant effects on the total amount.

What sum of money will amount to ₹6,400 in 4 years at a simple interest rate of 5% per annum?

Discover how to calculate the principal that will amount to ₹6,400 in 4 years at 5% simple interest. This problem involves key mathematical concepts like simple interest, algebraic equations, and is suitable for students in Grades 8-10.

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