An initial investment of $1000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?
A)10.29 years
B)9.29 years
C)9.90 years
D)10.90 years
E)1 year

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for continuous compounding:

A = Pe^(rt)

where A is the ending amount, P is the principal (initial investment), e is the base of the natural logarithm, r is the annual interest rate (as a decimal), and t is the time (in years).

We want to find the time it takes for the investment to double, which means we want to solve for t when A = 2P. Plugging in the given values, we get:

2P = Pe^(0.07t)

Dividing both sides by P and simplifying, we get:

2 = e^(0.07t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.07t

Solving for t, we get:

t = ln(2)/0.07 ≈ 9.90 years

Therefore, the answer is C, 9.90 years.

An Initial Investment of $1000 Grows at an Annual Interest