# Find the compound interest on rs 2000 at 20% pa for one and half years the interest being compounded half yearly? and quarterly?

2
by ekalavyaachanta
Compounded half yearly:
P = Rs 2,000. r = 20%
n = number of times compounded = 1.50 yrs / 0.50 yrs = 3 times
Sum = P (1+r/100)^n = 2, 000 (1 + 20/100)^3 = Rs 2,000 * 1.2^3
Compound interest = sum - P = Rs 2, 000 (1.2^3 - 1) = Rs 1, 456
compounded quarterly:
n = 1.50 yrs / 0.25 yrs = 6
Sum = Rs 2, 000 ( 1 + 20/100)^6 = Rs 2, 000 * 1.2^6
interest = Rs 3, 971.97
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Sorry. above there is a mistake.. rate of interest is only 10% for 6 months.
Compounded half yearly:
P = Rs 2,000. r = 20% per annum.. r = 10% per half year.
n = number of times compounded = 1.50 yrs / 0.50 yrs = 3 times
Sum = P (1+r/100)^n = 2, 000 (1 + 10/100)^3 = Rs 2,000 * 1.1^3
Compound interest = sum - P = Rs 2, 000 (1.1^3 - 1) = Rs 662
compounded quarterly:
n = 1.50 yrs / 0.25 yrs = 6
Sum = Rs 2, 000 ( 1 + 10/100)^6 = Rs 2, 000 * 1.1^6
compound interest = Rs 1, 543.12
the interests are : Rs 662, and Rs 1, 543.12 respectively.

2015-04-30T14:51:01+05:30

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p=Rs.2000
R=20% p.a
T=1 1/2 y.
2ND P compounded half yearly=
Rs.2000+Rs.2000*20/100*1/2
=200+2000
=Rs.2200
3RD:
Rs 2200+Rs.2200*20/100*1/2
=Rs.2420
4th and final (if compounded 1/2 yearly)
=Rs.2420+Rs.2420*20/100*1/2
=Rs.2662
CI=Rs.2662-2000=Rs.662
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iF IT IS Quarterly:
.p=Rs.2000
R=20% p.a
T=1 1/2 y.
2ND P compounded quarterly=
Rs.2000+Rs.2000*20/100*1/4
=100+2000
=Rs.2100
3RD:
Rs 2100+Rs.2100*20/100*1/4
=Rs.2205
4TH:
Rs.2205+Rs.2205*20/100*1/4
=2315.25
5TH:
Rs.2315.25+Rs.2315.25*20/100*1/4
=Rs.2431.0125
=Rs.2431.01(approx)
6th:
Rs.2431.01+Rs.2431.01*20/100*1/4
=Rs.2552.5605
=Rs.2552.56 (approx)
7th and last=
Rs.2552.56+Rs.2552.56*1/4*20/100
=2680.18 (approx)
CI=Rs.680.18

2015-04-30T16:07:40+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Compounded half yearly:

P = Rs 2,000. r = 20% per annum.. r = 10% per half year.
n = number of times compounded = 1.50 yrs / 0.50 yrs = 3 times
Sum = P (1+r/100)^n = 2, 000 (1 + 10/100)³ = Rs 2,000 * 1.1³
Compound interest = sum - P = Rs 2, 000 (1.1^3 - 1) = Rs 662

Compounded quarterly:

n = 1.50 yrs / 0.25 yrs = 6
Sum = Rs 2, 000 (1 + 10/100)⁶ = Rs 2, 000 * 1.1⁶
compound interest = Rs 1, 543.12

So the interests are : Rs 662, and Rs 1, 543.12 respectively.

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