A person receives a simple interest of ₹1000 on a principal amount at 5% per annum for a period of 4 years. Find the compound interest that would be earned on double the original principal amount over a 2-year period at the same rate of interest.

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To solve this problem, we need to first find the original principal amount and then calculate the compound interest on double this amount.

Step 1: Find the principal amount using the simple interest formula.
Simple Interest Formula: SI = (P × R × T)/100
Given: SI = ₹1000, R = 5%, T = 4 years

Rearranging to find P:
P = (SI × 100)/(R × T)
P = (1000 × 100)/(5 × 4)
P = 100000/20
P = ₹5000

Step 2: Calculate compound interest on twice the principal.
New Principal = 2 × ₹5000 = ₹10000
Using the compound interest formula: A = P(1 + R/100)^T

A = 10000(1 + 5/100)^2
A = 10000(1.05)^2
A = 10000 × 21/20 × 21/20
A = 10000 × 441/400
A = ₹11025[1]

Step 3: Find the compound interest.
Compound Interest = Final Amount - Principal
CI = ₹11025 - ₹10000 = ₹1025

Therefore, the compound interest earned on twice the principal would be ₹1025.

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