A principal sum of money invested under simple interest accumulates to ₹8000 after 2 years and further increases to ₹8800 after 3 years. What is the annual simple interest rate applied to this investment?

The correct option is 12.5%.

Let's break down the solution step-by-step to understand how the simple interest rate is calculated.

Step 1: Understand the given information

1. The principal sum accumulates to ₹8000 after 2 years. So, the Amount after 2 years ($A_2$) = ₹8000.
2. The amount further increases to ₹8800 after 3 years total (i.e., after 1 more year). So, the Amount after 3 years ($A_3$) = ₹8800.

Step 2: Find the Simple Interest for 1 year

In simple interest, the principal remains constant, which means the interest earned every year is identical.

The increase in amount from Year 2 to Year 3 is equal to the simple interest earned in that 1 year:

$\text{Simple Interest for 1 year (SI)}=A_3-A_2$

$\text{SI for 1 year}=8800-8000=\text{₹800}$

Step 3: Calculate the total Simple Interest earned in the first 2 years

Since the interest earned each year is ₹800:

$\text{Simple Interest for 2 years}=2\times 800=\text{₹1600}$

Step 4: Determine the Principal (P)

The total amount after 2 years includes the original Principal plus the 2 years of simple interest:

$\text{Amount after 2 years}=\text{Principal}+\text{Simple Interest for 2 years}$

$8000=P+1600$

$P=8000-1600=\text{₹6400}$

Step 5: Calculate the Annual Simple Interest Rate (R)

We use the standard simple interest formula:

$\text{SI}=\frac{P\times R\times T}{100}$

Substituting the values for 1 year ($\text{SI}=800$, $P=6400$, $T=1$):

$800=\frac{6400\times R\times 1}{100}$

$800=64\times R$

$R=\frac{800}{64}=12.5\%$

Thus, the annual simple interest rate applied to this investment is 12.5%.