Questions: If 10,000 is invested at 6% annual interest compounded yearly, what is the account balance after 4 years, assuming no additional deposits or withdrawals are made? a.) 12,689.86 b.) 12,704.89 c.) 12,624.77 d.) 12,667.70

Solution Steps

To find the account balance after a certain number of years with compound interest, we 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 (initial investment).
• \( r \) 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 for in years.

In this problem:

• \( P = 10,000 \)
• \( r = 0.06 \) (6% as a decimal)
• \( n = 1 \) (compounded yearly)
• \( t = 4 \) years

Substitute these values into the formula:

\[ A = 10,000 \left(1 + \frac{0.06}{1}\right)^{1 \times 4} \]

Calculate the expression inside the parentheses:

\[ 1 + \frac{0.06}{1} = 1.06 \]

Raise this to the power of 4:

\[ 1.06^4 \approx 1.2625 \]

Multiply by the principal amount:

\[ A = 10,000 \times 1.2625 = 12,625 \]

The calculated amount is $12,625.00. Compare this with the given options:

• a.) $12,689.86$
• b.) $12,704.89$
• c.) $12,624.77$
• d.) $12,667.70$

The closest option is c.) $12,624.77$.

Final Answer