A sum of ₹6,400 earns a compound interest of ₹1,008.80 in 18 months, when the interest is reckoned half-yearly. Find the rate of interest.
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Answered by
36
Rate of interest = 10%
Explanation:
Given: A sum of ₹6,400 earns a compound interest of ₹1,008.80 in 18 months, when the interest is reckoned half-yearly. Find the rate of interest.
Principal = Rs. 6400
Interest = 1008.80
Period = 18 months = 18 / 12 = 3 / 2 years
Interest reckoned half-yearly.
Amount = principal + interest = 7408.80
Substituting the values in the compound interest formula, we get:
A = P (1 + r/n)^nt
7408.80 = 6400 (1 + r/2)^(2*3/2)
7408.80 / 6400 = (1 + r/2)^3
1.157625 = (1 + r/2)^3
1 + r/2 = cube root of 1.157625 = 1.05
r/2 = 0.05
Therefore r = 0.1
Rate of interest = 0.1 * 100 = 10%
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