Question

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

Answer 1

Answer:

$t=14.2\ years$    

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

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  

$t=?\ years\\ P=\ 500,000\\ r=0.05\\n=1\\ A=\ 1,000,000$  

substitute in the formula above  and solve for t

$1,000,000=500,000(1+\frac{0.05}{1})^{(1)t}$

$2=(1.05})^{t}$  

Apply log both sides

$log(2)=log[(1.05})^{t}]$  

$log(2)=(t)log(1.05)$  

$t=log(2)/log(1.05)$  

$t=14.2\ years$