Investment rate

Question

how many years will it take for an initial investment of $40,000 to grow to $60,000? Assume a rate of interest of 19% compounded continuously.

Answer 1

Use the continuous compound interest formula, A = Pe ^rt

A =$60,000  P = $40,000, r = 0.19 and solve for t. Recall that e stands for the Napier's number (base of the natural logarithm) which is approximately 2.7183. 

 

Therefore, $60,000 = $40,000 e^0.19t Thus, 1.5 = e^0.19t

To solve for t is will be necessary to convert to a logarithmic solution

Then 0.19t = log_e 1.5, and t = log_e 1.5 / 0.19 = 2.14 years

Answer 2

The formula for continuous compounding is 

 

A = Pe^(rt)  

 

where A is the final amount, P is the principle (or initial amount), r is the rate (as a decimal) and t is time.  So we have

 

60000 = 40000*e^(0.19t)

1.5 = e^(0.19t)

 

Take the natural log ( ln ) of both sides

 

ln(1.5) = 0.19t

t = ln(1.5) / 0.19 = (0.405465)/(0.19) = 2.134 years