Question

Lee has invested $2800 in a venture company,he receives 6.5 % interest in a year,compounded continuously. how long will it take his money to double

Answer 1

Answer:

$t=10.66\ years$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$  

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  

e is the mathematical constant number

we have  

$t=?\ years\\ P=\ 2,800\\A=\ 5,600\\r=0.065$  

substitute in the formula above

$5,600=2,800(e)^{0.065t}$  

solve for t

simplify

$2=(e)^{0.065t}$  

Apply ln both sides

$ln(2)=ln[(e)^{0.065t}]$  

Apply property of logarithms

$ln(2)=(0.065t)ln(e)$  

$ln(e)=1$

$t=ln(2)/(0.065)$  

$t=10.66\ years$