Question

Find the doubling time of an investment earning 7% interest if interest is compounded continuously

Answer 1

Answer:

The doubling time of this investment would be 9.9 years.

Step-by-step explanation:

The appropriate equation for this compound interest is

A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.

If P doubles, then A = 2P

Thus, 2P = Pe^(0.07t)

Dividing both sides by P results in 2 = e^(0.07t)

Take the natural log of both sides:  ln 2 = 0.07t.

Then t = elapsed time = ln 2

                                       --------- = 0.69315/0.07 = 9.9

                                         0.07

The doubling time of this investment would be 9.9 years.