SOLUTION: 5-2 (Compound value solving for n) how many years will the following take? a. $500.00 to grow to $1,039.50 if invested at 5 percent compounded annually b. $35 to grow to $53.87 i

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Question 1107095: 5-2 (Compound value solving for n) how many years will the following take?
a. $500.00 to grow to $1,039.50 if invested at 5 percent compounded annually
b. $35 to grow to $53.87 if invested at 9 percent compounded annually
c. 100 to grow to $298.60 if invested at 20 percent compounded annually
d. $53 to grow to $78.76 if invested at 2 percent compounded annually

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.