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Find Compound Interest when interest is compounded QuarterlyCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! To find compound interest when interest is compounded quarterly, we use the following formula :A = P ( 1 + R/4 )^{4n} and C.I. = A – P Where, P = Principal R = Rate of interest p.a (per annum i.e annually) n = number of years. Examples : 1) Find the compound interest on $320,000 for one year at the rate of 20% p.a., if the interest rate is compounded quarterly. Solution: Here, P = $320,000, R = 20% p.a. and n = 1 year. ∴ Amount after 1 year = P ( 1 + R/4 ) ^{4n} = 320,000 x ( 1 + 0.20/4 ) ^{4 x 1} = 320,000 x ( 1 + 0.05) ^{4} = 320,000 x (1.05 ) ^{4} = 320,000 x 1.21550 = Rs. 388,962 ∴ Compound interest = 388,962 – 320,000 = 68,962 ________________________________________________________________ 2)Ryan deposited $ 7500 in a bank which pays him 12% interest p.a. compounded quarterly. What is the amount which he receives after 9 months? Solution: Here, P = $ 7500, R = 12% p.a. and n = 9 months = 9/12 year = 3/4 year ∴ Amount after 9 months = P ( 1 + R/100 ) ^{4n} = 7500 x ( 1 + 0.12/4 ) ^{4n} = 7500 x ( 1 + 0.03 ) ^{4 x 3/4 } = 7500 x ( 1.03) ^{3} = 7500 x 1.092727 = $ 8195.45 ________________________________________________________________ 3)Jacob deposited $ 9000 in a bank which pays him 8% interest p.a. compounded quarterly. What is the amount which he receives after 6 months? Solution: Here, P = $ 9000, R = 8% p.a. and n = 6 months = 6/12 year = 1/2 year ∴ Amount after 6 months = P ( 1 + R/100 ) ^{4n} = 9000 x ( 1 + 0.08/4 ) ^{4 x 1/2} = 9000 x ( 1 + 0.02 ) ^{2 } = 9000 x ( 1.02) ^{2} = 9363.6 = $ 9363.60 Compound Interest • Find Compound Interest when interest is compounded Half yearly • Find Compound Interest when interest is compounded Quarterly • Find CI when interest is compounded annually but Rates are different • Finding Principal • Finding Time Period of Investment • Finding Rate of Interest Covid19 has affected physical interactions between people. Don't let it affect your learning.
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