SOLUTION: Find the time needed to Reach an investment goal if you want to say 5000 before buying your first new car and you have 3000 right now tp invest at 3% interest compound monthley

Algebra ->  Equations -> SOLUTION: Find the time needed to Reach an investment goal if you want to say 5000 before buying your first new car and you have 3000 right now tp invest at 3% interest compound monthley       Log On


   

Question 1198391: Find the time needed to Reach an investment goal if you want to say 5000 before buying your first new car and you have 3000 right now tp invest at 3% interest compound monthley
Found 3 solutions by Theo, ewatrrr, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you can use a financial calculator or you can use the following formula.
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.

in your problem:
f = 5000
p = 3000
r = .03/12
n = number of months.

formula becomes:
5000 = 3000 * (1 + .03/12) ^ n
divide both sides of the equation by 3000 to get 5/3 = (1 + .03/12) ^ n
simplify to get 5/3 = 1.0025 ^ n
take the log of both sides of the equation to get:
log(5/3) = log(1.0025^n) which becomes:
log(5/3) = n * log(1.0025)
divide both sides of the equation by log(1.0025) to get:
log(5/3) / log(1.0025) = n
solve for n to get:
n = 204.585556.
confirm by replacing n with that and solving for f in the original equation to get:
f = 3000 * (1 + .03/12) ^ 204.585556 = 5000

the 3000 will grow to 5000 in 204.585556 months = 17.04879634 years.

if you used a calculator such as the one at https://arachnoid.com/finance/, you would get n = 204.59.
that's the same answer as from the formula, except rounded to 2 decimal places.

here are the results from using that calculator.



since the interest rate is compounded monthly, then you need to get the monthly interest rate and you are solving for the number of months.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
In General A%28t%29+=+P%281%2Br%2Fn%29%5E%28nt%29
for example: in one year: A = 3000(1.0025)^12 = $3091.25 rounded
in two years: A = 3000(1.025)^24 = $3185.27 rounded
in 17 years; A = 4992.70 rounded
A = Accumulated Amount = 5000
P= principal = 3000
r= annual rate = .03
n= periods per year = 12
t= years =
5000=+3000%281.0025%29%5E%2812t%29
+log%28+5%2F3%29%2F12log%281.0025%29+=+t = 17.0487 yr
compounding monthly:
1yr and .0487*12 = 17yr & 1mo (rounded up)

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Find the time needed to Reach an investment goal if you want to say 5000 before buying your first new car and you have 3000 right now tp invest at 3% interest compound monthley 
Correct answer: At the 17 year, 1-month, or 205th-month juncture.

Any other answer is UNACCEPTABLE!