Question

Find how many years it would take for an investment of $3600 to grow to $6900 at an annual interest rate of 4.3% compounded continuously.

Answer 1

Answer:

roughly 15 years

Step-by-step explanation:

The formula for continuous compounding is

A = Pe^(rt), where P is the initial amount (principal), r is the interest rate as a decimal fraction, and t is the number of years.  Here:

$6900 = $3600*e^(0.043*t).  Let's solve this for t.  To accomplish that,

take the natural log of both sides:

ln 6900 = ln 3600 + 0.043t.  Subtracting ln 3600 from both sides, we get:

8.839 = 8.189 + 0.043t, or    0.6506 = 0.043t.  Dividing both sides by 0.043 yields

      0.6506

t = --------------- = 15.13 years, or about 15 years 2 months, or roughly 15 years

         0.043