Question

an amount was lent for two years at the rate 20% per annum compounding annually .
compounding been done half yearly the interest would be increased by 241.

what was the amount (in Rs) lent?

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Answer 1

Answer:

Rs 10000

Step-by-step explanation:

an amount was lent for two years at the rate 20% per annum compounding annually .

compounding been done half yearly the interest would be increased by 241.

Let say Amount Lent  = P Rs

Rate of interest = R = 20% per annum

T = time in years

n = Compounding frequency in a year

Compound interest = P(1 + R/100n)^(nT) - P

T =2 Years n = 1

Compound interest = P ( 1 + 0.2)² - P  =  P * 1.2² - P

T =1 Years n = 2

Compound interest = P ( 1 + 0.1)⁴ - P  =  P * 1.1⁴ - P

Difference in Interest = P * 1.1⁴ - P - (P * 1.2² - P)

= P * 1.1⁴ - P * 1.2²

=P (1.21)² - P * 1.2²

= P  ( 1.21 + 1.2)(1.21 - 1.2)

= P (2.41)(.01)

= P 241 /10000

P 241 /10000 = 241

=> P = 10000

Amount lent = Rs 10000