Thread: 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?.

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 $\displaystyle t$.

If it is coumpounded anually would it be T/12 or for instance of it ask compounded quarterly T/4?

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 $\displaystyle t$.

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%

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.

great