Question

How long would it take you to double your money is the bank pays 3.6% interest, compounded
continuously?

Answer 1

Answer:

$t=19.25\ years$

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  

$t=?\ years\\P=x\\r=3.6\%=3.6/100=0.036\\A=2x$  

substitute in the formula above

$2x=x(e)^{0.036t}$  

solve for t

simplify

$2=(e)^{0.036t}$  

Apply ln both sides

$ln(2)=ln[(e)^{0.036t}]$

Applying property of exponents

$ln(2)=[0.036t]ln(e)$

Remember that ln(e) =1

$ln(2)=[0.036t]$

$t=ln(2)/[0.036]$

$t=19.25\ years$