Question

suppose that $4,600 is invested at 5.8% annuel insters rate compounded monthly how much money will be in the account in 7 months

Answer 1

After 7 months, a $4,600 investment at a 5.8% annual interest rate compounded monthly would grow to approximately $5,928.50.

To calculate the future value of an investment compounded monthly, you can use the formula:

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

Where:

- A is the future value of the investment/loan, including interest.

- P is the principal investment amount (the initial deposit or loan amount).

- r is the annual interest rate (as a decimal).

- n is the number of times that interest is compounded per unit t.

- t is the time the money is invested or borrowed for, in years.

In this case:

- P = $4,600,

- r = 0.058 (5.8% expressed as a decimal),

- n = 12 (compounded monthly),

-
`\(t = (7)/(12)\)` (7 months is equivalent to
`\( (7)/(12) \)` years).

Now plug these values into the formula:

`\[ A = 4600 \left(1 + (0.058)/(12)\right)^{12 * (7)/(12)} \]`

Calculate the expression to find the future value of the investment after 7 months.

`\[ A = 4600 \left(1 + (0.058)/(12)\right)^{12 * (7)/(12)} \]\[ A \approx 4600 \left(1 + 0.004833\right)^(0.5833) \]\[ A \approx 4600 * 1.291647 \]\[ A \approx 5928.50 \]`

Therefore, the future value of the investment after 7 months would be approximately $5,928.50.