shakira invests $500000 at 5% compound intwerest per annum . calculate how many years it takes for the value to double in value?

Answer:[tex]t=14.2\ years[/tex]    Step-by-step explanation:we know that    The compound interest formula is equal to  [tex]A=P(1+\frac{r}{n})^{nt}[/tex]  where  A is the Final Investment Value  P is the Principal amount of money to be invested  r is the rate of interest  in decimal t is Number of Time Periods  n is the number of times interest is compounded per year in this problem we have  [tex]t=?\ years\\ P=\$500,000\\ r=0.05\\n=1\\ A=\$1,000,000[/tex]  substitute in the formula above  and solve for t[tex]1,000,000=500,000(1+\frac{0.05}{1})^{(1)t}[/tex] [tex]2=(1.05})^{t}[/tex]   Apply log both sides[tex]log(2)=log[(1.05})^{t}][/tex]   [tex]log(2)=(t)log(1.05)[/tex]   [tex]t=log(2)/log(1.05)[/tex]   [tex]t=14.2\ years[/tex]