Answer: it will take 17.33 years to double.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e^(r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 425
A = 2 × 425 = 850
r = 4% = 4/100 = 0.04
Therefore,
850 = 425 x 2.7183^(0.04 x t)
850/425 = 2.7183^(0.04t)
2 = 2.7183^(0.04t)
Taking ln of both sides, it becomes
Ln 2 = 0.04t ln 2.7183
0.693 = 0.04t
t = 0.693/0.04
t = 17.325
