The formula for calculating continuously compounded interest is expressed as
A = Pe^rt
where
P represents the principal or initial amount
A represents the final amount after t years
r represents the interest rate
From the information given,
A = 70000
P = 20000
r = 14% = 14/100 = 0.14
By substituting these values into the formula, we have
70000 = 20000e^0.14t
Dividing both sides by 20000, we have
70000/20000 = 20000/20000e^0.14t
3.5 = e^0.14t
We would take the natural log of both sides. We have
ln 3.5 = lne^0.14t
Recall these rules of logarithm
lna^b = blna
lne = 1
By applying these rules, we have
ln 3.5 = 0.14tlne
ln 3.5 = 0.14t
0.14t = ln3.5
Dividing both sides by 0.14, wehave
0.14t/0.14 = ln3.5/0.14
t = 8.95
It will take approximately 8.95 years for an initial investment of $20,000 to grow to $70,000