Suppose your​ friend's parents invest $ 20 comma 000 in an account paying 6 % compounded annually. What will the balance be after 6 ​years?

Question

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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 find the balance of the investment after 6 years with an initial amount of $20,000 at an interest rate of 6% compounded annually, we 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).
• \( r \) is the annual interest rate (decimal).
• \( n \) is the number of years the money is invested or borrowed.

Given:

• \( P = 20,000 \)
• \( r = 6% = 0.06 \)
• \( n = 6 \)

Plugging these values into the formula, we get:

\[ A = 20000(1 + 0.06)^6 \]

Calculating this step-by-step:

1. Calculate \( 1 + 0.06 = 1.06 \).
2. Calculate \( 1.06^6 \).

Using a calculator:

\[ 1.06^6 \approx 1.418519 \]

3. Now, calculate \( A \):

\[ A = 20000 \times 1.418519 \approx 28370.38 \]

Thus, the balance in the account after 6 years will be approximately $28,370.38 (rounded to the nearest cent).