Solve the problem.
-How long will it take money to double if it is invested at 5.25%, compounded continuously? Round your answer to the nearest tenth.
A) 0.13 yr
B) 14 yr
C) 13.2 yr
D) 26.4 yr

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A represents the amount accumulated, P represents the principal invested, e represents Euler's number approximately equal to 2.71828, r represents the annual interest rate in decimal form, and t represents the time in years. We want to find out how long it will take for the investment to double, which means that the amount accumulated will be twice the principal invested (A = 2P). We can substitute these values into the formula and solve for t:

2P = Pe^(0.0525t)
2 = e^(0.0525t)
ln(2) = 0.0525t
t = ln(2)/0.0525
t ≈ 13.2 years

Therefore, the answer is choice C, 13.2 years, rounded to the nearest tenth. We can use the formula for continuous compounding, which is A = Pe^(rt), where A is the amount after time t, P is the principal (starting amount), r is the annual interest rate, and e is the mathematical constant approximately equal to 2.71828. We want to find the time it takes for the amount to double, which means we are looking for the value of t when A = 2P. Plugging in the given values, we get:

2P = Pe^(0.0525t)
2 = e^(0.0525t)
ln(2) = 0.0525t
t = ln(2)/0.0525
t ≈ 13.2

So it will take approximately 13.2 years for the money to double. The closest answer choice is C.

Solve the Problem. -How Long Will It Take Money to Double If It