If Frances invests $4,000 in her retirement account with a 5% return compounded 6 times a year, how much will she have in 5 years?

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Multiple Choice

If Frances invests $4,000 in her retirement account with a 5% return compounded 6 times a year, how much will she have in 5 years?

Explanation:
To determine how much Frances will have in her retirement account after 5 years, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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 number of years the money is invested or borrowed. Plugging in the values from the question: - \( P = 4000 \) - \( r = 0.05 \) (which is 5% expressed as a decimal) - \( n = 6 \) (since the interest is compounded 6 times a year) - \( t = 5 \) Now, we substitute these values into the formula: \[ A = 4000 \left(1 + \frac{0.05}{6}\right)^{6 \times 5} \] Calculating the components step-by-step:

To determine how much Frances will have in her retirement account after 5 years, we can use the formula for compound interest:

[ A = P \left(1 + \frac{r}{n}\right)^{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 number of years the money is invested or borrowed.

Plugging in the values from the question:

  • ( P = 4000 )

  • ( r = 0.05 ) (which is 5% expressed as a decimal)

  • ( n = 6 ) (since the interest is compounded 6 times a year)

  • ( t = 5 )

Now, we substitute these values into the formula:

[

A = 4000 \left(1 + \frac{0.05}{6}\right)^{6 \times 5}

]

Calculating the components step-by-step:

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