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Equal amounts of each ₹ 1,000 is lent to two persons for 3 years one @ 30% simple interest and second at 30% compound interest annually. By how much percent is the compound interest greater than the simple interest received in this 3 years duration.
Compound Interest after 3 years = Amount - Principal
= $$P\left(1+\dfrac{r}{100}\right)^3-P$$
= $$1000\left(1+\dfrac{30}{100}\right)^3-1000$$
= $$1000\left(1.3\right)^3-1000$$
= ₹ $$1197$$
Simple Interest after 3 years = $$\dfrac{1000\times\ 30\times\ 3}{100}$$ = ₹ $$900$$
So, required difference =₹ $$\left(1197-900\right)=297$$
So, required percentage = $$\dfrac{297}{900}\times\ 100=33\%$$
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