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)26.4 yr
C)13.2 yr
D)14 yr

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A=Pe^(rt), where A is the amount, P is the principal or starting amount, 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 t when the amount is double, so we can set up the equation 2P = Pe^(0.0525t) and simplify by dividing both sides by P to get 2 = e^(0.0525t). Taking the natural logarithm of both sides gives ln(2) = 0.0525t, and solving for t gives t = ln(2)/0.0525, which is approximately 13.2 years. Therefore, the answer is option C.

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