# Find Compound Interest when interest is compounded Half yearly

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 - Pwhere, 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

• 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