Question 1118761: What amount is accumulated after 3 years of P6,500 invested at a rate of 12% per year compounded semi annually.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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