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Question 1142172: Calculate the present value (principal) and the compound interest given: Compound Amount = $1,250 Term of Investment = 6 years Nominal rate = 6% Interest is compounded semiannually
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe you're saying that the future value is 1250 and that you want to know what the present value is.
under that assumption, the following formula applies.
f = p * (1 + r) ^ n
f is the futurevalue
p is the present value
r is the interest rate per time period
n is the number of time periods.
you are given that n = 6 years and that f = 1250.
you are also given that r = 6% per year.
if your interest is compounded semi-annually, then your time periods need to be in semi-annual periods.
6% per year / 2 = 3% per semi-annual period.
in the formula, you use the rate, not the percent.
3% / 100 = an interest rate .03 per semi-annual time period.
n = 6 years * 2 semi-annual periods per year = 12 semi-annual time periods.
the formula becomes 1250 = p * (1 + .03) ^ 12
solve for p to get p = 1250 / (1 + .03) ^ 12 to get p = 876.7248502.
confirm by replacing p in the original equation with that to get:
f = 876.7248502 * (1 + .03) ^ 12 = 1250.
this confirms the solution is correct.
the solution is the present value = 876.7248502.
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