SOLUTION: 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?

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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