Problema Solution
On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs.180. Find the sum lent out, if the rate of interest in both the cases is 10%.
Answer provided by our tutors
let
P = the principal (the sum lent out)
r = 0.10 or 10% the annual interest rate
t = 1 year
Simple Interest I = P*r*t
I = 0.10P
Compound Interest for a year, payable half-yearly
interest in the first half of the year: P*(0.10/2) = P*0.5
interest in the second half of the year: (P + P*0.5)*0.5
total interest is
P*0.05 + (P + P*0.5)*0.5 = P*0.05 + P*0.5(1 + 0.5) = P*0.5*(2 + 0.5)
the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs.180
P*0.5*(2 + 0.5) - 0.10P = 180
by solving for P we find
P = $156.52
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the sum lent is $156.52.