The difference between CI and SI of a certain sum of money is Rs.61 at 5% p.a. for three years when the interest is compounded annually. Find the sum of money.
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Answer:
Rs.8000
Step-by-step explanation:
P = initial amount
R = rate of interest per cent per year = 5
T = time period in years = 3
A = amount at the end of period T
Simple Interest
SI = Simple interest = (P*R*T)/100
SI = P*5*3/100 = 15P/100
SI = 0.15P ....(i)
Compound Interest
A = P(1 + R/100)^3
A = P(1 + 5/100)^3
A = P(1.05)^3
CI = Compound interest = A - P
=> CI = P(1.05)^3 - P
=> CI = P[(1.05)^3 - 1]
=> CI = 0.157625P ...(ii)
Given difference in CI and SI = 61
=> 0.157625P - 0.15P = 61
=> 0.007625P = 61
=> P = 61/0.007625
=> P = 8000
The initial amount (principal) is Rs.8000
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