Questions: Compute the total and annual returns on the following investment. You pay 5500 for a municipal bond. When it matures after 20 years, you receive 11,400. The total return is %. (Do not round until the final answer. Then round to one decimal place as needed.)

Compute the total and annual returns on the following investment. You pay 5500 for a municipal bond. When it matures after 20 years, you receive 11,400.

The total return is %.
(Do not round until the final answer. Then round to one decimal place as needed.)

Transcript text: Compute the total and annual returns on the following investment. You pay $\$ 5500$ for a municipal bond. When it matures after 20 years, you receive $\$ 11,400$. The total return is $\square$ $\%$. (Do not round until the final answer. Then round to one decimal place as needed.)

Solution

Solution Steps

Step 1: Calculate the Total Return

To find the total return on the investment, we calculate the percentage increase from the initial investment to the final amount received. The formula for total return is:

\[ \text{Total Return} = \left( \frac{\text{Final Amount} - \text{Initial Investment}}{\text{Initial Investment}} \right) \times 100 \]

Substituting the given values:

\[ \text{Total Return} = \left( \frac{11400 - 5500}{5500} \right) \times 100 = 107.2727\% \]

Rounding to one decimal place, the total return is $107.3\%$.

Step 2: Calculate the Annual Return

To find the annual return, we use the formula for compound interest to determine the equivalent yearly growth rate that would result in the total return over the investment period. The formula is:

\[ \text{Annual Return} = \left( \left( \frac{\text{Final Amount}}{\text{Initial Investment}} \right)^{\frac{1}{\text{Years}}} - 1 \right) \times 100 \]

Substituting the given values:

\[ \text{Annual Return} = \left( \left( \frac{11400}{5500} \right)^{\frac{1}{20}} - 1 \right) \times 100 = 3.6986\% \]

Rounding to one decimal place, the annual return is $3.7\%$.