Question

If $600 is deposited into a savings account which pays 4.8% interest, compound continuously (A = Pe^rt), how long will it take the money to triple. Round to the nearest tenth of a year.

Answer 1

Answer:

$22.9\ years$  

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  

$t=?\ years\\ P=\ 600\\ r=0.048\\ A=\ 600*3=\ 1,800$  

substitute in the formula above  and solve for t

$\ 1,800=\ 600(e)^{0.048t}$  

Simplify

$3=(e)^{0.048t}$  

apply ln both sides

Remember that

$ln(e)=1$

$ln(3)=0.048t*ln(e)$  

$ln(3)=0.048t$  

$t=ln(3)/0.048=22.9\ years$