# Compound interest

• May 12th 2013, 01:27 AM
Gurp925
Compound interest
I have this log question,

How long will it take an intiatial investment to grow by 50 % in each of the following cases:

A) 5% per year, i wont write b, c because they are more or less the same.

my problem is i dont know how to set up the problem this is what i see

Initial amount= ?
final amount?
growth rate= 1.05 (1+.5)
T=?
95%=A(1.05%)^t

I do not know how to incorporate the rate at which it compounds nor do i know how to add the 5%

Can i just assume A?.
• May 12th 2013, 02:14 AM
MarkFL
Re: Compound interest
If the investment has grown by 50%, then the amount $\displaystyle A$ the investment is worth is $\displaystyle A=1.5P$ where $\displaystyle P$ is the principal. Compounded annually at an interest rate of $\displaystyle r$, we would write:

$\displaystyle 1.5P=P(1+r)^t$

Now, divide through by $\displaystyle P$ to get:

$\displaystyle 1.5=(1+r)^t$

Now you can use logs to solve for $\displaystyle t$.
• May 12th 2013, 01:06 PM
Gurp925
Re: Compound interest
If it is coumpounded anually would it be T/12 or for instance of it ask compounded quarterly T/4?
Quote:

Originally Posted by MarkFL
If the investment has grown by 50%, then the amount $\displaystyle A$ the investment is worth is $\displaystyle A=1.5P$ where $\displaystyle P$ is the principal. Compounded annually at an interest rate of $\displaystyle r$, we would write:

$\displaystyle 1.5P=P(1+r)^t$

Now, divide through by $\displaystyle P$ to get:

$\displaystyle 1.5=(1+r)^t$

Now you can use logs to solve for $\displaystyle t$.

• May 12th 2013, 02:37 PM
Shakarri
Re: Compound interest
Since r is interest per year, t will be in years

The answer should be 8.31 years. If you got 5% compounded monthly from a bank then the answer would be 8.31 months to increase your investment by 50%
• May 12th 2013, 03:16 PM
MarkFL
Re: Compound interest
Quote:

Originally Posted by Gurp925
If it is compounded annually would it be T/12 or for instance of it ask compounded quarterly T/4?

A more general formula is:

$\displaystyle A=P\left(1+\frac{r}{n} \right)^{nt}$

where $\displaystyle n$ is the number of times the interest is compounded annually.
• May 13th 2013, 12:44 AM
Gurp925
Re: Compound interest
great