SOLUTION: Matt invest $500 into an account with a 7.5% interest rate compounded yearly. How long will it be until the account has a value of $2500?

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Question 1072014: Matt invest $500 into an account with a 7.5% interest rate compounded yearly. How long will it be until the account has a value of $2500?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
f = p * (1+r) ^ n

f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.

your time period is years.

you are given that:

i = 7.5% per year / 100 = .075 per year.

p = 500

f = 2500

f = p * (1+r) ^ n becomes 2500 = 500 * 1.075 ^ n

divide both sides of this equation by 500 to get:

2500 / 500 = 1.075 ^ n

simplify to get:

5 = 1.075 ^ n

take the log of both sides of this equation to get:

log(5) = log(1.075 ^ n)

since log(a^b) = b * log(a), your equation becomes:

log(5) = n * log(1.075)

divide both sides of this equation by log(1.075) to get:

log(5) / log(1.075) = n

solve for n to get:

n = 22.25419233

confirm by replacing n in the original equation and evaluating to see that the equation is true.

2500 = 500 * 1.075 ^ n becomes 2500 = 500 * 1.075 ^ 22.25419233.

evaluate to get 2500 = 2500.

this confirms the solution is good.

the solution is that it will take 22.25419233 year for 500 to become 2500 at an interest rate of 7.5% compounded annually.