Thread: logarithmic word problem

Hello, here is my problem:

Alex invests $50,000 at an interest rate of 0.7% compounded monthly. Laura invests $40,000 at 9.5% compounded annually. After how many years will the two investments be equal in value?

okay so this is what I have so far

50,000 x (.07x12)^n=x

40,000 x .095^n=x

I am not really sure how to set up the equation and I'm pretty sure I started off wrong, help is much appreciated!

Thank you!
Dan

The 1st amount gets multiplied by 1.007 each month and the 2nd amount by 1.095 each year.

it should have been: 50,000 x (1.07^n)12=x and 40,000 x (1.095 ^n)=x I think im figuring it out. Biffboy, i think you ment to write 1.07

If the interest rate is 0.7% we multiply by 1.007. If you meant 7% we multiply by 1.07. In your question you said 0.7%
Also n years =12n months so with the 50000 the index will be 12n

The reason i cant figure it out is because it has two variables. In the answers n= 10.6, but if you sub that in the x variable in each equation are different when they should be the same according to the question in the first post. I am clearly missing something...

The first rate can't be 7% per month as amounts then would never be equal. So it must be 0.7% and you should be multiplying by 1.007^(12n)

I made a mistake writing the problem, sorry it is 7% not 0.7%, and 9.5%. My bad... Thank you for you help though, I'm busting out the calculator right now!

Originally Posted by Dwahl

Hello, here is my problem:

Alex invests $50,000 at an interest rate of 0.7% compounded monthly. Laura invests $40,000 at 9.5% compounded annually. After how many years will the two investments be equal in value?

okay so this is what I have so far

50,000 x (.07x12)^n=x

No "7% compounded monthly" does NOT mean 7% per month. It is still 7% per year which is percent per month. In n years, there are, of course, 12n months so it will be

40,000 x .095^n=x

And this should have been
Set them equal and solve for n.

I am not really sure how to set up the equation and I'm pretty sure I started off wrong, help is much appreciated!

Thank you!
Dan

this is what i have so far, thanks for all your help guys, I really appreciate it!

50000 (1.00583)^12n = 40000 (1.095)^n

log(50000 x 1.00583^12n) = log(40000 x1.095^n)

log 50000 + log 1.00583^12n = log 40000 + log 1.095^n

log 50000 + 12n log 1.00583= log 40000+ n log 1.095

and this is sort of where i get a bit lost, below is what i did.

log 50000 - log 40000= -12n log 1.00583 + n log 1.095

Im not sure how to simplify it anymore. so i tried this

__ log 50000- log 40000____ = n+n
-12 + log 1.00583 + log 1.095

Can I get a little more help simplifying it, because I know I did it wrong :/ thanks again!

Last line wrong. In the previous line write the right hand side as n(log1.095-12log1.00583)