Question 1172998
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.