Answer: the interest rate is 6%
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,
A = $4482
P = 1000
t = 25 years
Therefore,
4482 = 1000 x 2.7183^(r x 25)
4482/1000 = 2.7183^25r
4.482 = 2.7183^25r
Taking ln of both sides, it becomes
Ln 4.482 = 25rLn2.7183
1.5 = 25r
r = 1.5/25 = 0.06
r = 0.06 × 100 = 6%
