Rachit invests ₹12,000 for a 2-year period at a certain rate of simple interest per annum. Prasad invests ₹12,000 for a 2-year period at the same rate of interest per annum as Rachit, but in Prasad's case the interest is compounded annually. Find the rate of interest per annum if Prasad receives ₹172.80 more as interest than Rachit at the end of the 2-year period.
Solution
In the question, Rachit and Prasad invested the same amount for the same time duration and same rate of interest. But one is invested on simple interest and another one is one compound interest. Their difference of interest is also given.
So difference of interests = $$principal\left(\frac{rate}{100}\right)^2$$
$$172.80 = 12000 \left(\frac{rate}{100}\right)^2$$
$$\frac{172.80}{12000}=\left(\frac{rate}{100}\right)^2$$
$$\frac{1728}{120000}=\left(\frac{rate}{100}\right)^2$$$$\frac{144}{10000}=\left(\frac{rate}{100}\right)^2$$
$$\left(\frac{12}{100}\right)^2=\left(\frac{rate}{100}\right)^2$$
So after comparing both of the sides, the rate of interest = 12%
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