Question

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Part 1
Suppose your​ friend's parents invest $ 10 comma 000 in an account paying 5 % compounded annually. What will the balance be after 6 ​years?
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Part 1
The account balance will be ​$
  
enter your response here
​(Round to the nearest cent as​ needed.)

Answer 1

To calculate the balance of an investment that is compounded annually, you can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

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 years the money is invested or borrowed for.

In this case:
- \( P = 10,000 \)
- \( r = 0.05 \) (5% as a decimal)
- \( n = 6 \)

Now plug the values into the formula:

\[
A = 10,000(1 + 0.05)^6
\]

Calculate \( (1 + 0.05)^6 \):

\[
(1.05)^6 \approx 1.340095
\]

Now calculate \( A \):

\[
A \approx 10,000 \times 1.340095 \approx 13,400.95
\]

So, the balance after 6 years will be approximately:

\[
\text{The account balance will be } \mathbf{13,400.95}
\]

(Rounded to the nearest cent as needed.)