Question
Suppose that $10 comma 000 is invested at 7% interest. Find the amount of money in the account after 9 years if the interest is compounded annually.
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Question content area right
Part 1
If interest is compounded annually, what is the amount of money after tequals9 years?
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.
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Question content area right
Part 1
If interest is compounded annually, what is the amount of money after tequals9 years?
Answers
GPT-4o mini
To find the amount of money in the account after 9 years with an initial investment of $10,000 at an interest rate of 7% compounded annually, you can use the formula for compound interest:
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of money in the account after \( t \) years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the number of years the money is invested or borrowed.
Given:
- \( P = 10,000 \)
- \( r = 0.07 \) (7% as a decimal)
- \( t = 9 \)
Now plug in the values:
\[
A = 10,000(1 + 0.07)^9
\]
\[
A = 10,000(1.07)^9
\]
\[
A = 10,000 \times 1.838459
\]
\[
A \approx 18,384.59
\]
So, the amount of money in the account after 9 years is approximately **$18,384.59**.
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of money in the account after \( t \) years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the number of years the money is invested or borrowed.
Given:
- \( P = 10,000 \)
- \( r = 0.07 \) (7% as a decimal)
- \( t = 9 \)
Now plug in the values:
\[
A = 10,000(1 + 0.07)^9
\]
\[
A = 10,000(1.07)^9
\]
\[
A = 10,000 \times 1.838459
\]
\[
A \approx 18,384.59
\]
So, the amount of money in the account after 9 years is approximately **$18,384.59**.