If $$ \$ 5,000 $$ is invested at $$ 8 \% $$ annual interest compounded monthly, what is the account balance after 5 years, assuming no additional deposits or withdrawals are made a.) $$ \$ 7,346.64 $$ b.) $$ \$ 7,429.74 $$ c.) $$ \$ 7,449.23 $$ d.) $$ \$ 7,401.22 $$

Question

UpStudy AI · Accepted Answer

To determine the account balance after 5 years with an initial investment of \$5,000 at an annual interest rate of 8% compounded monthly, we can use the compound interest formula:

$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

Where:
- $$ A $$ is the amount of money accumulated after $$ t $$ years, including interest.
- $$ P $$ is the principal amount (\$5,000).
- $$ r $$ is the annual interest rate (8% or 0.08).
- $$ n $$ is the number of times that interest is compounded per year (12 for monthly).
- $$ t $$ is the time the money is invested for in years (5 years).

Plugging in the values:

$$
A = 5000 \left(1 + \frac{0.08}{12}\right)^{12 \times 5}
$$

$$
A = 5000 \left(1 + 0.0066667\right)^{60}
$$

$$
A = 5000 \left(1.0066667\right)^{60}
$$

Calculating the compound factor:

$$
\left(1.0066667\right)^{60} \approx 1.48923
$$

So,

$$
A \approx 5000 \times 1.48923 = 7446.15
$$

Comparing this with the given options:

- **c.) \$7,449.23** is the closest to our calculated value of \$7,446.15.

**Answer:**  
**c.) \$7,449.23**
The account balance after 5 years is approximately \$7,449.23.

If is invested at annual interest compounded
monthly, what is the account balance after 5 years,
assuming no additional deposits or withdrawals are made
a.)
b.)
c.)
d.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Arithmetic Questions

If is invested at annual interest compounded monthly, what is the account balance after 5 years, assuming no additional deposits or withdrawals are made a.) b.) c.) d.)