SOLUTION: How would you solve the questions: How long will it take for $1400 dollars to grow to $11,900 at an interest rate of 2.3% if the interested is compounded quarterly? I am taking

Question 1054609: How would you solve the questions:
How long will it take for $1400 dollars to grow to $11,900 at an interest rate of 2.3% if the interested is compounded quarterly? I am taking the amount and dividing it by the initial investment. My next step has been to plug the following into my TI 84 calculator:
log(1+.023)8.5
Can you tell me what I am doing wrong? I get 8.6 years but the correct answer should be 20.65 years.
Thank you
Found 3 solutions by josmiceli, addingup, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Find in yrs
------------------------------

Take the log base 10 of both sides

I get a huge number
----------------------
20.65 yrs doesn't seem to work

??
Unless I messed up at the start
Are you sure all the data is correct?

Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
P =initial principal 1,400
n = number of times the interest is compounded per year (in your case 4)
F = future amount after time t 11,900
r = annual nominal interest rate 2.3%
t = number of years we'll find out
We need to use the following financial formula:
t =ln(F/p)/(ln(1+r/n)n)
t = ln(11,900/1,400)/(ln(1+(0.023/4))4)
t = (ln 8.5)/((ln 1.00575)*4) do the operations and you'll get 93.31
-------------------------------
check:
1,400(1+(0.023/4)^4*93.31 =
1,400(1.00575)^4*93.31
1,400(1.00575)^373.24 = 11,899.0155
As you see I lost a few cents in the rounding of the numbers, but the answer is correct.
:
John
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

How would you solve the questions:
How long will it take for $1400 dollars to grow to $11,900 at an interest rate of 2.3% if the interested is compounded quarterly? I am taking the amount and dividing it by the initial investment. My next step has been to plug the following into my TI 84 calculator:
log(1+.023)8.5
Can you tell me what I am doing wrong? I get 8.6 years but the correct answer should be 20.65 years.
Thank you

It CANNOT be 20.65 years. That's IMPOSSIBLE! It's just too short a time!
You must be either looking at the wrong answer or failed to include the correct figures.

------ Substituting $11,900 for A, $1,400 for P, .023 for i, and 4 (quarterly) for m
------ Dividing both sides by $1,400, and simplifying

------- Converting to LOGARITHMIC form
------ Applying change of base

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