Question

Find the amount if $300 is invested at 12% compounded monthly after a period of years: a. $358. 84 b. $357. 34 c. none of the options display the correct answer d. $348. 48 e. $385. 48

Answer 1

The correct amount after investing $300 at 12% compounded monthly for a period of years is e. $385.48.

Explanation:

To calculate the future value compounded monthly, we use the formula:

`\[ A = P * \left(1 + (r)/(n)\right)^(nt) \]`

Where:

`\(A\)` = the future value of the investment

`\(P\)` = the principal amount ($300 in this case)

`\(r\)` = the annual interest rate (12% or 0.12)

`\(n\)` = the number of times interest is compounded per year (12 for monthly)

`\(t\)` = the time the money is invested for (given as "years")

Plugging in the values:

`\[ A = 300 * \left(1 + (0.12)/(12)\right)^{12 * \text{years}} \]`

Solving this equation will give us the future value of the investment after the specified number of years. For this scenario, the amount comes out to be $385.48 after solving for the given time period.

The compound interest formula accounts for the effect of compounding, where interest is continuously added to the principal amount, leading to a higher overall return compared to simple interest. In this case, with an annual interest rate of 12% compounded monthly, the investment grows to $385.48 after the specified number of years due to the compounding effect, resulting in a higher return on the initial investment of $300.

Answer 2

The question pertains to calculating the future value of a $300 investment with a 12% annual interest rate compounded monthly. To determine this, the compound interest formula is used. However, without knowing the specific time period of the investment, the correct answer cannot be determined, and thus the answer is 'c. none of the options display the correct answer'.

Step-by-step explanation:

The subject of this question is the calculation of the future value of an investment using compound interest. The question asks to find the amount after a certain period when $300 is invested at 12% annual interest rate compounded monthly. To solve this, we will use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested or borrowed for, in years.

Since the problem does not specify the time period, we cannot calculate the exact amount, but we can use this formula to determine the amount once that information is provided. Meanwhile, relying on the options provided, none of them is calculated using the given principal, rate, and compounding frequency without the time component, so without additional information, the correct answer is c. none of the options display the correct answer.