Interest: how long to triple investment

[fdragon]

OK so its like this...
How long will it take to triple your money if you invest it at a rate of 6%. State in years rounded to the nearest thousandth, in years and months, and show the equation used.

.....compounded annually? ______,______,_______
.....compounded semiannually? _____,______,_____
.....compounded quarterly? _____,______,______
.....compounded monthly? ______,______,_______
.....compounded daily? ______,_______,______
.....compounded continously? ______,_______._______

Which option would be the better investment for the consumer?

...... my teach gave me an equation.... A= P(1+[r/n])^nt for compound equations
...... and for continuous.... A= Pe^rt

and....
A= Final Amount
P=Principle (Amount invested)
r= Interest Rate
n= number of times each year
t= time in years

I have no clue how to even begin lol!!! Ahhh!! :shock:

 

[stapel]

A good way to begin would be to plug the given information into the given equations.

For instance, given "A = P(1 + r/n)^nt", an unknown initial investment "P", a rate of, say, 8%, weekly compounding, and a requirement to double the investment, you would do the following:

. . . . .2P = P(1 + 0.08/52)^52t

. . . . .2 = (1 + 0.08/52)^52t

. . . . .ln(2) = 52t ln(1 + 0.08/52)

. . . . .ln(2) / ln(1 + 0.08/52) = 52t

Divide through by 52, and evaluate in your calculator for the value of t.

The same method will work for all of your examples.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[fdragon]

Ok not sure If I did this right but this is what I tried for annually....

A = P(1 + r/n)nt

3 = 1(1 + .06/1)^1t

ln 3 = 1t ln ( 1 + .06/1)

ln 3/ ln (1 + .06/1) = 1t

18.85 = 1t

18.85 = t

Is that right??? Can you use log instead of ln ? why are there three spaces in the question???[/tex]

 

[tkhunny]

1*t = t -- Don't write the "1". It is confusing.

"log" and "ln" should be interchangeable, as long as you know you are using the most useful, logarithm Base e.

There are three spaces because you have been asked three questions:
1) State in years rounded to the nearest thousandth,
2) in years and months, and
3) show the equation used.

 

[fdragon]

OK I see now..... my friends boyfriend did it and we turned it in and I got the same answer he did but I still wanna know how to do it anyway!
I'll work on it later tonight and post what I got.