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Ritika Mistry
Asked: 2022-11-04T21:47:47+05:30 In:

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. 2,211
2. Rs. 2,121
3. Rs. 2,122
4. Rs. 2,112

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. 2,211
2. Rs. 2,121
3. Rs. 2,122
4. Rs. 2,112
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1 Answer

  1. 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

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