SOLUTION: Find out how long it takes a ​$2900 investment to earn ​$500 interest if it is invested at 8​% compounded monthly. Round to the nearest tenth of a year.

Algebra ->  Finance -> SOLUTION: Find out how long it takes a ​$2900 investment to earn ​$500 interest if it is invested at 8​% compounded monthly. Round to the nearest tenth of a year.       Log On


   

Question 1113287: Find out how long it takes a ​$2900 investment to earn ​$500 interest if it is invested at 8​% compounded monthly. Round to the nearest tenth of a year.
Answer by Theo(13342) About Me  (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.

to find the interest earned, you would then subtract the present value from the future value.

the formula for that would be:

i = f - p

solve this equation for f to get:

f = p + i

in your problem:

p = 2900
f = p + i = 2900 + 500 = 3400
i = .08 / 12 per month.
n = number of months.

your equation becomes:

3400 = 2900 * (1 + .08/12) ^ n

divide both sides of this equation by 2900 to get:

3400 / 2900 = (1 + .08/12) ^ n

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

log(3400 / 2900) = log((1 +.08/12) ^ n)

since log (b^x) = x * log(b), this equation becomes:

log(3400 / 2900) = n * log(1 + .08/12)

solve for n to get:

n = log(3400 / 2900) / log(1 + .08/12) = 23.93914847 months.

replace n in the original equation with that to confirm the solution is correct.

original equation becomes 3400 = 2900 * (1 + .08/12) ^ 23.93914847.

this results in 3400 = 3400, confirming the solution is correct.

23.93914847 months / 12 = 1.994929039 years.

round this to the nearest tenth of a year to get 2 years.