Compute the interest on 12000 for 2 years at 20 per annum when 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

Free

IBPS RRB Office Assistant Prelims Full Mock Test

80 Questions 80 Marks 45 Mins

Given:

Principal is Rs. 12000 

Rate of interest, r = 20%

Numbers of years, n = 1.5 yeras

Calculation:

Amount compounded half-yearly,

\(\Rightarrow 12000 \times {\left( {1 + 10/100} \right)^{2 \times 1.5}}\)

⇒ 12000 × (1.1)3

⇒ 12000 × 1.331

⇒ 15972

Therefore the correct answer is 15972.

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