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

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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

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