Questions: Decide whether the following statement makes (or is clearly true) or does not make sense (or is clearly false). Explain. My financial advisor showed me that I could reach my retirement goal with deposits of 244 per month and an average return of 5%. But I don't want to deposit that much of my paycheck, so I'm going to reach the same goal by getting an average annual return of 11% instead. Choose the correct answer below. A. This does not make sense because you cannot choose your own annual rate of return. B. This makes sense because 11% of 244 is greater than 5% of 244. C. This does not make sense because 244 is not a lot of money to earn interest off of. D. This makes sense because an average annual return of 11% is greater than 5%.

Decide whether the following statement makes (or is clearly true) or does not make sense (or is clearly false). Explain.
My financial advisor showed me that I could reach my retirement goal with deposits of 244 per month and an average return of 5%. But I don't want to deposit that much of my paycheck, so I'm going to reach the same goal by getting an average annual return of 11% instead.

Choose the correct answer below.
A. This does not make sense because you cannot choose your own annual rate of return.
B. This makes sense because 11% of 244 is greater than 5% of 244.
C. This does not make sense because 244 is not a lot of money to earn interest off of.
D. This makes sense because an average annual return of 11% is greater than 5%.

Transcript text: Decide whether the following statement makes (or is clearly true) or does not make sense (or is clearly false). Explain. My financial advisor showed me that I could reach my retirement goal with deposits of $\$ 244$ per month and an average return of $5 \%$. But I don't want to deposit that much of my paycheck, so l'm going to reach the same goal by getting an average annual return of $11 \%$ instead. Choose the correct answer below. A. This does not make sense because you cannot choose your own annual rate of return. B. This makes sense because $11 \%$ of $\$ 244$ is greater than $5 \%$ of $\$ 244$. C. This does not make sense because $\$ 244$ is not a lot of money to earn interest off of. D. This makes sense because an average annual return of $11 \%$ is greater than $5 \%$.

Solution

Solution Steps

To determine whether the statement makes sense, we need to understand the relationship between the deposit amount, the rate of return, and the final retirement goal. The key point is that a higher rate of return can potentially reduce the amount needed to be deposited each month to reach the same retirement goal. However, the feasibility of achieving a higher rate of return consistently is another matter.

Step 1: Calculate Future Value with 5% Return

To find the future value of the retirement goal with a monthly deposit of $ \$244 $ and an annual return of $ 5\% $, we use the future value formula for an annuity:

\[ FV = P \cdot \frac{(1 + r/n)^{nt} - 1}{r/n} \]

Where:

$ P = 244 $
$ r = 0.05 $
$ n = 12 $ (monthly deposits)
$ t = 30 $

Calculating this gives:

\[ FV = 244 \cdot \frac{(1 + 0.05/12)^{12 \cdot 30} - 1}{0.05/12} \approx 203071.11 \]

Step 2: Calculate Required Monthly Deposit with 11% Return

Next, we need to determine the required monthly deposit to achieve the same future value with an annual return of $ 11\% $. We rearrange the future value formula to solve for $ P $:

\[ P = \frac{FV \cdot \frac{r/n}{(1 + r/n)^{nt} - 1}}{1} \]

Using $ FV \approx 203071.11 $, $ r = 0.11 $, $ n = 12 $, and $ t = 30 $:

\[ P \approx \frac{203071.11 \cdot \frac{0.11/12}{(1 + 0.11/12)^{12 \cdot 30} - 1}}{1} \approx 72.41 \]

Final Answer

The required monthly deposit with an $ 11\% $ return is significantly lower than the $ \$244 $ deposit at $ 5\% $. Thus, the statement makes sense because an average annual return of $ 11\% $ is greater than $ 5\% $.

The answer is $ \boxed{D} $.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!