What will be the effective rate of interest for the first year, if the rate of interest is 40% p.a. compounded semi-annually?
40%
42%
43%
44%
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The effective rate of interest is 44 %.
We have to find the effective rate of interest for first year , if the rate of interest is 40 % p.a compounded semi - annually.
method 1 :
Here,
rate of interest , r = 40 % per annum.
∴ the rate of interest per half year , r' = r/2 = 40/2 = 20 % per half year.
∵ time , t = 1 year = 2 half years
now effective rate of interest is given by, R = r' + r' + (r' × r')/100
= 20 % + 20 % + (20 × 20)/100 %
= 40 % + 400/100 %
= 40 % + 4 %
= 44 %
Therefore the effective rate of interest is 44 %.
method 2 : Let principal = P , rate , r = 20 % per half year , time, n = 2 half year
so, A = P(1 + r/100)ⁿ
= P(1 + 20/100)²
= P(6/5)²
= 36P/25
CI = A - P = 36P/25 - P = 11P/25
so effective rate of interest = CI/P × 100
= (11P/25)/P × 100
= 11/25 × 100
= 44 %
Therefore the effective rate of interest is 44 %.
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