Questions: An investor bought stock for 50,000. Ten years later, the stock was sold for 60,000. If interest is compounded continuously, what annual nominal rate of interest did the original 50,000 investment earn?

An investor bought stock for 50,000. Ten years later, the stock was sold for 60,000. If interest is compounded continuously, what annual nominal rate of interest did the original 50,000 investment earn?

Transcript text: An investor bought stock for $\$ 50,000$. Ten years later, the stock was sold for $\$ 60,000$. If interest is compounded continuously, what annual nominal rate of interest did the original $\$ 50,000$ investment earn?

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the annual nominal rate of interest $r$ for an investment compounded continuously. The formula to use is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the initial principal balance, $r$ is the annual nominal interest rate, $t$ is the time in years, and $e$ is the base of the natural logarithm.

Step 2: Rearrange the Formula to Solve for $r$

To find $r$, we rearrange the formula to $r = \frac{1}{t} \ln\left(\frac{A}{P}\right)$.

Step 3: Substitute the Known Values into the Formula

Substituting the given values into the formula, we get $r = \frac1{10} \ln\left(\frac{60000}{50000}\right)$.

Step 4: Perform the Calculation

Performing the calculation, $r = 0.0182$.