Question 1118761
12% compounded semi-annually would be equal to 12/2 = 6% per semi-annual period.


the formula for compound interest is f = p * (1 + r) ^ n.


f is the future value
p is the present value
r is the interest rate per time period (months in this case).
n is the number of time periods (months in this case).


in your problem, p = 6500, r = .12/2 = .06 per semi-annual period, n = 3 * 2 = 6 semi-annual periods.


the formula becomes 6500 = p * (1 + .06) ^ 6.


solve for p to get p = 6500 / ((1 + .06) ^ 6)


you get p = 4582.243513.


6500 = 4582.243513 * (1 + .06) ^ 6 becomes 6500 = 6500, confirming the solution is correct.


in these compounded interest rate calculations, if you are given the annual interest rate and the number of years, then:


interest rate per time period = annual interest rate divided by number of compounding periods per year.


number of time periods = number of years times number of compounding periods per year.


in your problem, you spefied compounding semi-annually.


that means 2 compounding periods per year.


12% / 2 = 6% per semi-annual period.
3 years * 2 = 6 semi-annual periods.


in the formula, the interest rate percent is divided by 100 to get interest rate.


12% per year is there .12 per year.
divide that by 2 and you get an interest rate of .06 per semi-annual period.