The difference between compound interest and simple interest in the 3rd year at a rate of 10% is 77.5 rupees is??
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Answer:
Rs. 2500. Provided here is the difference that is there between CI (Compound Interest) and SI (Simple Interest), which is given as Rs. 77.5. Hence, CI - SI = 77.5 We have to determine CI and SI first. Let us say the Principle(P) amount is Rs. x, Time in years (n) = 3, the interest rate (r) = 10%. Therefore, SI = p*n*r/100. SI = x * 10 * 3/100. So, SI = 0.3 x. To calculate CI = P * [(1 + r)^n - 1]. Substituting the values, CI = P * [(1 + (10/100))^3 - 1] (taking that the interest compounds yearly). So, CI = x * [(1.1)^3 - 1]. Hence, CI = x * [1.331 - 1]. Thus, CI = 0.331 x. It is based on the given formula. Now, to find out the CI using concept. Compound interest says that the interest for a year gets summed up to its principle. i.e. an interest of the 1st year sums to its principle and on this combined principle, the interest of the second year can be found out and so forth. Hence, the Principle of 1st year = Rs. x. The first year interest = x * 10 /100 = 0.1 x. The Principle of 2nd year = x + 0.1 x = 1.1 x. Thus, the second year interest = 1.1 x * 10 /100 = 0.11 x. The Principle of third year = 1.1 x + 0.11 x = 1.21 x. So, the third year interest = 1.21 x * 10 /100 = 0.121 x. Therefore, the total interest = 1st year + 2nd year + 3rd year. CI = 0.1 x + 0.11 x 0.121 x. CI = 0.331 x. Now, after we substitute it in the equation, CI - SI = 77.5, we get, 0.331 x - 0.3 x = 77.5, i.e., 0.031 x = 77.5. Hence, x = 77.5 /0.031. Thus, x = Rs. 2500. Therefore the Principle amount is Rs. 2500.