SOLUTION: 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 year

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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) About Me  (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.