Math, asked by ekalavyaachanta, 1 year ago

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

kvnmurty: 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
============

kvnmurty: Sorry. above there is a mistake.. rate of interest is only 10% for 6 months.

kvnmurty: 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

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

Answers

Answered by AcharyaVII

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
===================================================
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

Answered by kvnmurty

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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