Question 1107095
i'll do one.
you can use the same procedure on the rest.


the formula to use is f = p * (1 + r/c) ^ (n*c)


f is the future value
p is the present value
r is the annual interest rate
c is the number of compounding periods per year.
n is the number of years.


since you are dealing with annual compounding, then c = 1 and the formula simplifies to f = p * (1 + r) ^ n


i'll do the first problem:


start with 1039.50 = 500 * (1 + .05) ^ n


you use the interest rate in these formulas, not the percent.
interest rate = percent divided by 100.


divide both sides of this equation by 500 to get 1039.50/500 = (1 + .05) ^ n


take the log of both sides of the equation to get log(1039.50/500) = log(1.05)^n


since log(1.05)^n is equal to n * log(1.05), the equation becomes log(1039.50/500) = n * log(1.05).


divide both sides of the equation by log(1.05) to get log(1039.50/500) / log(1.05) = n


solve for n to get n = 15.00070806


confirm by replacing n in the original equation to get 1039.50 = 500 * (1.05)^15.00070806


simplify to get 1039.50 = 1039.5


this confirms the solution is correct.


your solutions for this and the other problems should be:


a. 15.00070806
b. 5.003912776
c. 6.00002939
d. 20.00307001


follow the procedure i used for the first problem and you should get the answer shown for the other three problems.