Answer :

To find the rate at which ₹ 7000 will amount to ₹ 7945 in 3 years, we can use the simple interest formula. The simple interest formula for the amount is:

[tex]\[ \text{Final Amount} = \text{Principal} \times (1 + \text{Rate} \times \text{Time}) \][/tex]

Where:
- Principal is the original amount of money, which is ₹ 7000.
- Final Amount is the amount after interest, which is ₹ 7945.
- Rate is the interest rate per year, expressed as a decimal.
- Time is the time period in years, which is 3 years.

Here's how we can calculate the rate step by step:

1. Write the formula for the final amount:

[tex]\[ 7945 = 7000 \times (1 + \text{Rate} \times 3) \][/tex]

2. Divide both sides by the principal to isolate the term with the rate:

[tex]\[ 1 + \text{Rate} \times 3 = \frac{7945}{7000} \][/tex]

3. Calculate the division:

[tex]\[ 1 + \text{Rate} \times 3 = 1.135 \][/tex]

4. Subtract 1 from both sides to solve for the product of rate and time:

[tex]\[ \text{Rate} \times 3 = 0.135 \][/tex]

5. Divide both sides by the time (3) to solve for the rate:

[tex]\[ \text{Rate} = \frac{0.135}{3} \][/tex]

6. Calculate the rate:

[tex]\[ \text{Rate} = 0.045 \][/tex]

The rate at which ₹ 7000 will amount to ₹ 7945 in 3 years is 0.045, or 4.5% per year.

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