Question

lee has invested $2800 in a venture company. he receives 6.5% interest a year, compounded continuously. How long will it take his money to double?

Answer 1

It'll take 10.6638 years to double his money.

Explanation:

Since the invested capital is compounded continuosly we need to use the apropriate formula shown below:

M = C*e^(r*t)

Where M is the final value, C is the initial value, r is the rate of interest and t is the total time elapsed. In this case we want to double our investment, since the amount invested was 2800, then we need to have a final value of 2*2800 = 5600. Applying these values to the formula:

5600 = 2800*e^(0.065*t)

2800*e^(0.065*t) = 5600

e^(0.065*t) = 5600/2800

e^(0.065*t) = 2

ln(e^(0.065*t)) = ln(2)

0.065*t = ln(2)

t = ln(2)/0.065 = 10.6638 years

It'll take 10.6638 years to double his money.