How long will it take for ₹6000 invested at the rate of 1.5% per annum simple interest to amount to ₹7650?

Steps to Solve

1. Identify known values We know the principal amount $P = 6000$ (initial investment), the final amount $A = 7650$ (amount after interest), and the interest rate $r = 1.5% = 0.015$ (annual interest rate). We need to find the time $t$ in years.

2. Use the simple interest formula The formula for simple interest is given by: $$ A = P(1 + rt) $$ where $A$ is the final amount, $P$ is the principal, $r$ is the rate of interest per year, and $t$ is the time in years.

3. Rearranging the formula to solve for time We need to isolate $t$ in the equation: $$ A = P(1 + rt) $$ First, divide both sides by $P$: $$ \frac{A}{P} = 1 + rt $$ Then, subtract 1 from both sides: $$ \frac{A}{P} - 1 = rt $$ Finally, solve for $t$: $$ t = \frac{\frac{A}{P} - 1}{r} $$

4. Substitute the known values into the formula Now, substitute $A = 7650$, $P = 6000$, and $r = 0.015$ into the equation: $$ t = \frac{\frac{7650}{6000} - 1}{0.015} $$

5. Calculate the value of time Now, calculate the left side:

6. Calculate $ \frac{7650}{6000} = 1.275$.

7. Subtract 1: $1.275 - 1 = 0.275$.

8. Finally, divide by $0.015$: $$ t = \frac{0.275}{0.015} = 18.3333... \approx 18.33\text{ years} $$