An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?
A)17.33 years
B)18.33 years
C)18.00 years
D)17.00 years
E)1 year

Question

Quizplus · Accepted Answer

The continuous compound interest formula is given by: 
A = Pe^(rt)
where A is the final amount, P is the initial principal, e is the mathematical constant, r is the interest rate, and t is the time.

If we want to double the initial investment, then we need to find the time it takes for the final amount to be twice the initial amount.

2P = Pe^(rt) 
2 = e^(0.04t) 
ln(2) = 0.04t 
t = ln(2)/0.04 
t = 17.33 years (rounded to two decimal places)

Therefore, it will take approximately 17.33 years for the initial investment of $2000 to double at an annual interest rate of 4% compounded continuously.

An Initial Investment of $2000 Grows at an Annual Interest