Question

The simple interest on a sum of money for 3 years at 20/3 per annum is ₹6750. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?​

Answer 1

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Answer 2

Answer: Rs. 7210

Step-by-step explanation:

Given: Simple interest; S.I. = Rs. 6750 , Time; t= 3 years, Rate; R= $\dfrac{20}{3}\%$

Now as we know

$S.I. = \dfrac{P\times R \times T}{100} \\\\\Rightarrow 6750 = \dfrac{P\times \dfrac{20}{3} \times 3}{100} \\\\\Rightarrow 6750\times 100 = P\times 20 \\\\\Rightarrow P= Rs. 33750$

Now we have to find the compound interest

Therefore

$A= P(1+\dfrac{R}{100} )^3\\\\\Rightarrow A= 33750(1+\dfrac{20}{3\times 100} )^3=33750(1+\dfrac{1}{15} )^3\\\\=33750\times \dfrac{16}{15} \times \dfrac{16}{15} \times \dfrac{16}{15} = Rs. 40960$

Compound Interest = A- P =  Rs. 40960 - Rs. 33750= Rs. 7210

Hence, the compound interest is Rs. 7210