Questions: Use the continuous compound interest formula to find the indicated value. A = 84,000; P = 68,294; r = 6.9%; t = ? t = years (Do not round until the final answer. Then round to two decimal places as needed.)

Solution Steps

We get \(\frac{A}{P} = e^{rt}\) which simplifies to \(\frac{84000}{68294} = e^{rt}\). In this case, \(\frac{84000}{68294} = 1.23\).

We get \(\ln\left(\frac{84000}{68294}\right) = rt\) which simplifies to \(\ln(1.23) = rt\). In this case, \(\ln(1.23) = 0.21\).

We get \(t = \frac{\ln\left(\frac{84000}{68294}\right)}{r}\) which simplifies to \(t = \frac{\ln(1.23)}{0.069}\). In this case, \(t = 3\) years.

Final Answer: