Question 1172998: A 35,000 principal earned an interest of P8, 500 at the end of 7 years. At what nominal rate, compounded annually, was it invested?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
p is the principal
f is the future value
r is the interest rate per time period
n is the number of time periods.
the interest rate per year is divided by the number of compounding periods per year to get the interest rate per time period.
r / 1 = r.
the number of years is multiplied by the number of compounding periods per year to get the number of time periods.
7 * 1 = 7
the interest earned was 8,500.
the principal was 35,000.
the future value became 35,000 + 8,500 = 43,500.
the formula becomes:
43,500 = 35,000 * (1 + r) ^ 7
divide both sides of the formula by 35,000 to get:
43,500 / 35,000 = (1 + r) ^ 7
take the 7th root of both sides of the equation to get:
(43,500 / 35,000) ^ (1/7) = 1 + r
solve for r to get:
r = (43,500 / 35,000) ^ (1/7) - 1 = .0315463451.
that's the interest rate per time period.
since the time period is in years, that's the interest rate per year.
confirm by replacing r in the original equation to get:
43,500 = 35,000 * (1 + .0315463451) ^ 7 = 43,500.
this confirms the solution is good.
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