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Find Compound Interest when interest is compounded Half yearlyCovid19 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 half yearly, we use the following formula.A = P ( 1 + r/2)^{2n} and C.I = A  P where, P = principal R = rate in percent p.a.( per annum i.e. annually) n = number of years. Examples : 1) Compute the compound interest on $12,000 for 2 years ate 20% p.a. when compounded halfyearly. Solution : Here, P = $12,000, R = 20% and n = 2 years. Amount after 2 years = P ( 1 + r/2) ^{2n} = 12,000 ( 1 + 0.20/2) ^{2 x 2} = 12,000 ( 1 + 0.1) ^{4} = 12,000 (1.1) ^{4} = 12,000 x 1.4641 Amount = $ 17569.20 ∴ C.I = A  P C.I = 17569.20  12000 C.I = $ 5569.20 _______________________________________________________________ 2) Find the compound interest on $1,000 at the rate of 10% p.a. for 18 months when interest is compounded halfyearly. Solution : Here, P = $1,000, R = 10% and n = 18 months = 18/12 = 3/2 years. Amount after 2 years = P ( 1 + r/2) ^{2n} = 1,000 ( 1 + 0.10 /2) ^{2 x 3/2} = 1,000 ( 1 + 0.05) ^{6/2} = 1,000 (1.05) ^{3} = 1,000 x 1.157625 Amount = $ 1157.625 ∴ C.I = A  P C.I = 1157.625  1000 C.I = $ 157.625 ________________________________________________________________________ 3) What sum will become $9,724.05 in 2 years, if the rate of interest is 10% compounded half yearly? Solution : Here, A = $9,724.05, R = 10% and n = 2years , P =?. Amount after 2 years = P ( 1 + r/2) ^{2n} 9,724.05= P ( 1 + 0.10 /2) ^{2 x 2} 9,724.05= P ( 1 + 0.05) ^{4} 9,724.05= P (1.05) ^{4} 9,724.05= P x 1.21550625 P = 9,724.05/1.21550625 P = $ 8000 Compound Interest ( CI ) • 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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