# Find Compound Interest when interest is compounded Half yearly

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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 half-yearly. 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
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2) Find the compound interest on $1,000 at the rate of 10% p.a. for 18 months when interest is compounded half-yearly. 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
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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