capital money of rs 31250 become rs 35152 after 3/2 yesr with interest when the interest was adjusted for each six months .what is the annual rate of interest?
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Answer:
8% Compound interest per annum
Step-by-step explanation:
Principle amount P = rs. 31250
Amount with interest A = rs. 35152.
Period = 3/2 years = 1.5 years.
Iterest adjusted for each six months.
∴ Interest period n = 1.5 / 0.5 = 3
Let the interest = r % per annum.
for six months, interest rate = r/2
Compound interst is given by
A = P [1 + r]^n
∴ 35152 = 31250 [ 1 + (r/2)]^3
(as interestcalculated six monthly, the rate is considered for 6 months,)
∴ 35152 ÷ 31250 = [1+ (r/2)]^3
∴ ∛1.124864 = 1+ r/2
∴ 1.04 = 1 + r/2
∴ r/2 = 0.04
∴ r = 0.08
∴ r = 8%
Annual rate of interest = 8%
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