SOLUTION: 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

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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