Answer :

arnav98
A = P ( 1 + r/2)2n and C.I = A - P 
vivek2001
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 

I've given 2 questions hope u'll understand it by observing it.

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