Question

1) Compute the compound interest on $12,000 for 2 years ate 20% p.a. when compounded half-yearly.
2) Find the compound interest on $1,000 at the rate of 10% p.a. for 18 months when interest is compounded half-yearly.

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Answer 1

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 

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 

Answer 2

Answer:

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Step-by-step explanation:

1) 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

_________________

2) 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