how long to the nearest year will it take an investment in Germany to double its value if the interest is compounded every six months

Question

tkhunny · Answer

There is not enough  information to answer this question as presented.  An interest rate is required.

kropot72 · Answer

$$A=P(1+r)^{t}$$
When interest is compounded annually the above equation applies, where A is the amount after t years, P is the principal, r is the annual interest rate expressed as a decimal and t is the time in years.
When the interest is compounded every six months the equation becomes:
$$A=P(1+\frac{r}{2})^{t}$$
where t is the number of six monthly intervals.
For the principal to double we get:
$$\frac{A}{P}=2=(1+\frac{r}{2})^{t}$$
Taking logs of both sides:
$$t \times \ln (1+\frac{r}{2})=\ln 2$$
$$t=\frac{\ln (1+\frac{r}{2})}{\ln 2}$$
Whenthe value of t is found it needs to be haved to find the number of years.