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- 1. Compound Interest • You have learnt about Simple Interest. As we have seen, interest is calculated at the end of term (may be for 2, 3 or more years) applying SI = PTR/100 where P is Principal, R is Rate of interest and T is Time in years. Now we will try to understand Compound Interest. Say , a certain sum of money is deposited or lent at compound interest for 3 years. We can not calculate interest after 3 years as we do in case of SI. We will find Interest at the end of each term ( may be 1 year, 6 months or 3 months as will be instructed) applying I = PTR/100 where T = 1 year or ½ year or ¼ year . Interest found above will be added to Principal taken there to find Amount at the end of that term. This Process is called Compounding. It will be done till the last term. ** There are three terms of compounding : Annual, Half-yearly and Quarterly eg. For time period of 3 years we have to do the same 3 times in case of Annual compounding, 6 times in case of Half-yearly compounding and 12 times in case of Quarterly compounding. Let us take an arbitrary problem where a sum P1 was deposited for 2 years at annual CI of R %. We have to find total C I and Amount after 2 years. See the Flowchart to work out: Step -1 Interest for first year ( C I1 ) = P1TR/100 . [ T = 1 Year] Step – 2 Amount after one year (A1) = P1 + C I1 [* This amount will be taken as principal (P2) for next term] Step – 3 Interest for second year ( C I2 ) = P2TR/100 [T = 1 Year] Step – 4 Amount after 2 years (A2) = P2 + C I2 Thus, total C I = C I1 + C I2 or is also = A2 – P1 ** For half-yearly compounding it should be done after every 6 months.
- 2. Compound Interest • The process we have followed above is tedious enough and time taking. We may do the same thing applying a formula: • Amount A = P ( 1 + R/100) N Where N is total number of compounding Case – 1 For Annual compounding, A = P ( 1 + R/100) T Case – 2 For Half-yearly compounding, A = P ( 1 + R/200) 2T Case – 3 For Quarterly compounding, A = P ( 1 + R/400) 4T Total C I = A - P Where P is Principal, R is annual Rate of interest, T is Time in years. Let us try to understand with a problem . Mr. Roy lent ₹ 2000 for 2 years at 10 % CI compounded annually. Find the interest he received after 2 years. Had it been lent at same rate of interest compounded half-yearly, how much more interest he would receive? P = ₹2000, T = 2 years, R = 10 % p.a. For annual compounding, A = P ( 1 + R/100) T = 2000(1 + 10/100)2 =2000 x 11/10 x11/10 = ₹2420 ie Total C I when compounded annually = 2420 – 2000 =₹ 420. For half-yearly compounding, A = P ( 1 + R/200) 2T = 2000(1 + 10/200)4 = 2000 x (21/20)4 = ₹2431 ie Total C I = A – P = 2431 – 2000 = ₹431 He would earn more C I by 431 – 420 = ₹11.