An investor deposited sum Y in Plan Alpha, which yields simple interest at a rate of 15% per annum for a duration of 4 years, earning an interest amount of Rs. 3600. If an amount of Rs. (Y + 1000) is invested in Plan Beta offering compound interest at 20% per annum compounded annually for 2 years, determine the interest earned from Plan Beta.

Correct Answer: Rs. 3080

Step-by-Step Explanation:

Step 1: Find the value of sum Y from Plan Alpha
For Plan Alpha, simple interest (SI) is calculated using the formula:

$\text{Simple Interest (SI)}=\frac{P\times R\times T}{100}$

From the given information for Plan Alpha:
Principal ($P$) = $Y$
Rate of interest ($R$) = 15% per annum
Time period ($T$) = 4 years
Simple Interest ($\text{SI}$) = Rs. 3600

Substituting these values into the simple interest formula:

$3600=\frac{Y\times 15\times 4}{100}$

$3600=\frac{60Y}{100}$

$3600=0.6Y$

$Y=\frac{3600}{0.6}=6000$

Thus, the deposited sum $Y$ is Rs. 6000.

Step 2: Determine the interest earned from Plan Beta
The amount invested in Plan Beta is $\text{Rs.}(Y+1000)$:

$\text{Principal for Plan Beta}=6000+1000=\text{Rs. 7000}$

Given details for Plan Beta:
Principal ($P$) = Rs. 7000
Compound interest rate ($R$) = 20% per annum
Time period ($n$) = 2 years (compounded annually)

The compound interest (CI) formula is:

$\text{Compound Interest (CI)}=P\times \left[{\left(1+\frac{R}{100}\right)}^n-1\right]$

Substituting the given values into the formula:

$\text{CI}=7000\times \left[{\left(1+\frac{20}{100}\right)}^2-1\right]$

$\text{CI}=7000\times \left[{\left(1.2\right)}^2-1\right]$

$\text{CI}=7000\times \left[1.44-1\right]$

$\text{CI}=7000\times 0.44=3080$

Therefore, the interest earned from Plan Beta is Rs. 3080.