Question

Charles invests $425 in a savings account that pays interest at an annual rate of 4 percent, compounded continuously. Approximately how much time will it take for his investment to double?

Answer 1

Answer: it will take 17.33 years to double.

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e^(r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 425

A = 2 × 425 = 850

r = 4% = 4/100 = 0.04

Therefore,

850 = 425 x 2.7183^(0.04 x t)

850/425 = 2.7183^(0.04t)

2 = 2.7183^(0.04t)

Taking ln of both sides, it becomes

Ln 2 = 0.04t ln 2.7183

0.693 = 0.04t

t = 0.693/0.04

t = 17.325