Answer:
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.
A) From the information given,
P = $800
r = 4.5% = 4.5/100 = 0.045
t = 5 years
Therefore,
A = 800 x e^(0.045 x 5)
A = 800 x e^(0.225)
A = $1002
B) For it to double,
A = 2 × 800 = 1600
Therefore,
1600 = 800 x e^(0.045 x t)
1600/800 = e^(0.045t)
2 = e^(0.045t)
Taking ln of both sides, it becomes
Ln2 = 0.045t
0.693 = 0.045t
t = 0.693/0.045
t = 15.4 years
