Question
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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Question content area right
Part 1
If interest is compounded annually, what is the amount of money after tequals9 years?
.
.
.
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 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**.
\[
A = P(1 + r)^t
\]
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**.
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