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Question 1037145: The sum of money which when given on compound interest at 18%per annum would fetch Rs 960 more when the interest is payable half yearly than when it was payable annually for 2 years ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula you need to use is:
f = p * (1+r)^n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
when your interest rate is 18% per year and you are compounding yearly for 2 years, you get:
r = 18% / 100 = .18 per year
n = 2 years
when your interest rate is 18% per year and you are compounding every half a year for 2 years, you get:
r = 18% / 100 = .18 per year / 2 = .09 per half year.
n = 2 years * 2 half periods per year = 4 half years.
the formula for yearly compounding becomes f = p * 1.18^2.
the formula for half yearly compounding becomes f = p * 1.09^4.
when you are compounding every half a year, the future value will be 960 more than when you are compounding once a year.
you get:
f = p * 1.18^2 for annual compounding.
f + 960 = p * 1.09^4 for half year compounding.
if you subtract the first equation from the second, you get:
960 = p * 1.09^4 - p * 1.18^2
factor out the p and you get 960 = p * (1.09^4 - 1.18^2)
divide both sides of the equation by (1.09^4 - 1.18^2) and you get:
960 / (1.09^4 - 1.18^2) = p
solve for p to get p = 960 / (1.09^4 - 1.18^2) = 50047.93654.
that's your solution.
50047.93654 * 1.18^2 = 69686.74684
50047.93654 * 1.09^4 = 70646.74684
subtract the first one from the second and you get 960.
this confirms the solution is correct.
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