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?

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: