The simple interest accrued on an amount of Rs. 45000/- after 2 years at a certain rate of interest is 13500/-. What will be the compound interest accrued on the same amount in the same number years at the same rate of interest?a)Rs. 14,512.50b)Rs. 14,521.80c)Rs. 14,515.30d)Rs. 14,518.90e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Given:
Principal amount (P) = Rs. 45000/-
Time (t) = 2 years
Simple interest (SI) = Rs. 13500/-

To find: Compound interest (CI) for the same amount, time, and rate of interest

Formulae used:
Simple Interest (SI) = (P * R * t) / 100
Compound Interest (CI) = P * [(1 + R/100) ^ t - 1]

Where,
P = Principal amount
R = Rate of interest
t = Time in years

Calculation:
From the given data, we can calculate the rate of interest.

SI = (P * R * t) / 100
13500 = (45000 * R * 2) / 100
R = (13500 * 100) / (45000 * 2)
R = 15%

Now, we can use the compound interest formula to calculate the CI.

CI = P * [(1 + R/100) ^ t - 1]
CI = 45000 * [(1 + 15/100) ^ 2 - 1]
CI = 45000 * [1.3225 - 1]
CI = 45000 * 0.3225
CI = Rs. 14,512.50 (approx)

Therefore, the compound interest accrued on the amount of Rs. 45000/- after 2 years at the rate of 15% is Rs. 14,512.50/-. Hence, option (a) is the correct answer.

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