Answer: it will take 20.83 years.
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 = 9900
A = 22800
r = 4% = 4/100 = 0.04
Therefore,
22800 = 9900 x 2.7183^(0.04 x t)
22800/9900 = 2.7183^0.04t
2.3 = 2.7183^0.04t
Taking ln of both sides, it becomes
Ln 2.3 = 0.04t ln2.7183
0.833 = 0.04t
t = 0.833/0.04
t = 20.83 years
