Suppose that ​$90 comma 000 is invested at 5​% interest. Find the amount of money in the account after 9 years if the interest is compounded annually.

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Part 1
If interest is compounded​ annually, what is the amount of money after tequals9 ​years?

Answer 1

To find the amount of money in the account after 9 years with annual compounding interest, we can use the formula for compound interest:

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

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).
• \( t \) is the number of years the money is invested or borrowed.

Given:

• \( P = 90,000 \)
• \( r = 5% = 0.05 \)
• \( t = 9 \)

Plugging in the values:

\[ A = 90,000(1 + 0.05)^9 \]

Calculating \( (1 + 0.05)^9 \):

\[ A = 90,000(1.05)^9 \]

Now calculate \( (1.05)^9 \):

\[ (1.05)^9 \approx 1.551328 \]

Now, substituting this back into the equation for \( A \):

\[ A \approx 90,000 \times 1.551328 \approx 139,619.52 \]

Thus, the amount of money in the account after 9 years is approximately $139,619.52.