An investor secured a business loan under a tiered simple interest arrangement: 6% per annum for the initial 4 years, 8% per annum for the subsequent 3 years, and 10% per annum for any period exceeding 7 years. If the total interest accumulated at the end of 9 years amounted to ₹4,760, what was the principal amount borrowed?

The correct answer is ₹7,000.

Step-by-Step Explanation:

1. Understand the Problem:

Let the principal amount borrowed be $P$.

The interest is calculated using simple interest over different time periods with tiered interest rates for a total duration of 9 years.

2. Break Down the Time Periods and Rates:

• First Period: Initial 4 years at an interest rate of 6% per annum.

$R_1=6\%$, $T_1=4\text{years}$

• Second Period: Subsequent 3 years at an interest rate of 8% per annum.

$R_2=8\%$, $T_2=3\text{years}$

• Third Period: The remaining period exceeding 7 years up to 9 years.

Remaining time: $T_3=9-7=2\text{years}$ at an interest rate of 10% per annum ($R_3=10\%$).

3. Formula for Total Simple Interest:

The total simple interest ($\text{SI}$) accumulated over the 9 years is the sum of simple interest from each of the three periods:

$\text{Total SI}=\frac{P\times R_1\times T_1}{100}+\frac{P\times R_2\times T_2}{100}+\frac{P\times R_3\times T_3}{100}$

We can factor out $\frac{P}{100}$:

$\text{Total SI}=\frac{P}{100}\times (R_1{T}_1+R_2{T}_2+R_3{T}_3)$

4. Substitute the Values:

Given that Total SI = ₹4,760:

$4760=\frac{P}{100}\times \left(\right(6\times 4)+(8\times 3)+(10\times 2\left)\right)$

$4760=\frac{P}{100}\times (24+24+20)$

$4760=\frac{P}{100}\times 68$

5. Solve for Principal Amount ($P$):

$P=\frac{4760\times 100}{68}$

Dividing 4760 by 68:

$4760÷68=70$

$P=70\times 100=7000$

Therefore, the principal amount borrowed by the investor was ₹7,000.