The compound interest accrued on a sum of Rs. 4400 at the end of 2 yea

1.	The compound interest accrued on a sum of Rs. 4400 at the end of 2 years is Rs. 1,119.36. What would be the simple interest on the sum at the same rate for double the time?1. Rs. 2,2112. Rs. 2,1213. Rs. 2,1224. Rs. 2,112
Answer» Correct Answer - Option 4 : Rs. 2,112 Given: Principal Amount (P) = Rs. 4400 Time Period (T) = 2 years Compound Interest after two years (CI) = 1119.36 Formulae Used: If Principal = P, Time period = T, and Rate of Interest = R; Compound Interest (CI) = {P [1 + (R/100)]T} - P; and Simple Interest (SI) = (P × R × T)/100 Calculation: Using the formula for CI, we can obtain the rate of interest (R) as: Compound Interest (CI) = {P [1 + (R/100)]T} - P ⇒ 1119.36 = {4400 × [1 + (R/100)]2} - 4400 ⇒ 5519.36/4400 = [(100 + R)/100]² ⇒ (100 + R)² = 1.2544 × 10000 ⇒ (100 + R) = 112 ⇒ R = 12% Now, for calculating the Simple Interest, Rate of Interest remains the same, so Rate = R Time period doubles, so T = 4 years Hence, we can calculate the value of Simple Interest (SI), as: SI = (4400 × 12 × 4)/100 ⇒ SI = Rs. 2112 ∴ The simple interest on the sum at the same rate for double the time is Rs. 2112

The compound interest accrued on a sum of Rs. 4400 at the end of 2 years is Rs. 1,119.36. What would be the simple interest on the sum at the same rate for double the time?1. Rs. 2,2112. Rs. 2,1213. Rs. 2,1224. Rs. 2,112

Answer» Correct Answer - Option 4 : Rs. 2,112

Given:

Principal Amount (P) = Rs. 4400

Time Period (T) = 2 years

Compound Interest after two years (CI) = 1119.36

Formulae Used:

If Principal = P, Time period = T, and Rate of Interest = R;

Compound Interest (CI) = {P [1 + (R/100)]T} - P; and

Simple Interest (SI) = (P × R × T)/100

Calculation:

Using the formula for CI, we can obtain the rate of interest (R) as:

Compound Interest (CI) = {P [1 + (R/100)]T} - P

⇒ 1119.36 = {4400 × [1 + (R/100)]2} - 4400

⇒ 5519.36/4400 = [(100 + R)/100]²

⇒ (100 + R)² = 1.2544 × 10000

⇒ (100 + R) = 112

⇒ R = 12%

Now, for calculating the Simple Interest,

Rate of Interest remains the same, so Rate = R

Time period doubles, so T = 4 years

Hence, we can calculate the value of Simple Interest (SI), as:

SI = (4400 × 12 × 4)/100

⇒ SI = Rs. 2112

∴ The simple interest on the sum at the same rate for double the time is Rs. 2112