How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.
A) 9.86 year(s)
B) 9.90 year(s)
C) 9.92 year(s)
D) 9.84 year(s)
E) 9.88 year(s)

Question

How long will it take an investment of $5,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places. ​
A) 9.86 year(s)
B) 9.90 year(s)
C) 9.92 year(s)
D) 9.84 year(s)
E) 9.88 year(s)

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the amount of money at time t, P is the principal (initial investment), e is the constant 2.71828..., r is the annual interest rate (as a decimal), and t is the time in years.

We want to find t when A = 2P and P = $5000 and r = 0.07. Substituting these values into the formula, we get:

2P = Pe^(0.07t)
Dividing both sides by P, we get:
2 = e^(0.07t)
Taking the natural logarithm (ln) of both sides, we get:
ln(2) = 0.07t
Dividing both sides by 0.07, we get:
t ≈ 9.90 years (rounded to two decimal places)

Therefore, it will take approximately 9.90 years for the investment to double. The best choice is B.

How Long Will It Take an Investment of $5,000 to Double