Questions: How many years will it take for an initial investment of 20,000 to grow to 50,000? Assume a rate of interest of 18% compounded continuously. It will take about years for the investment to grow to 50,000. (Round to two decimal places as needed.)

How many years will it take for an initial investment of 20,000 to grow to 50,000? Assume a rate of interest of 18% compounded continuously.

It will take about years for the investment to grow to 50,000.
(Round to two decimal places as needed.)

Transcript text: How many years will it take for an initial investment of $\$ 20,000$ to grow to $\$ 50,000$ ? Assume a rate of interest of $18 \%$ compounded continuously. It will take about $\square$ years for the investment to grow to $\$ 50,000$. (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the ratio $A/P$

To find how many times the initial investment needs to grow to reach the future value, we calculate the ratio $A/P = 50000/20000 = 2.5$.

Step 2: Take the natural logarithm of this ratio

The natural logarithm of the ratio $\ln(2.5)$ gives us the exponent to which $e$ must be raised to achieve this growth, which is $\ln(2.5) = 0.916$.

Step 3: Divide this result by the annual interest rate $r$ to find the number of years $t$

Dividing the natural logarithm of the ratio by the annual interest rate $r = 0.18$, we find the number of years: $t = \frac{\ln(2.5)}{0.18} = 5.09$.

Final Answer: It will take approximately 5.09 years for the initial investment to grow to the future value under the condition of continuous compounding at an annual interest rate of 18%.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!