Calculation of half-yerarly compound interest

2
by rehman

2014-08-07T21:43:43+05:30
A = P ( 1 + r/2)2n and C.I = A - P
2014-08-07T21:45:11+05:30
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.