Question 1037145
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.