Question
Which of the following expressions can be used to calculate the final amount of a 6-year loan of $5,324 with a compound interest rate of 6.7% compounded yearly?
$5,324(1+0.067)6
$5,324 0.067 6
$5,324(1+0.67)6
$5,324(1+6.7)6
Answers
Answered by
GPT-4o mini
To calculate the final amount of a loan with compound interest, you can use the formula:
\[ A = P(1 + r)^n \]
where:
- \( A \) is the final amount,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the interest rate (as a decimal), and
- \( n \) is the number of years.
For your loan of $5,324 with a compound interest rate of 6.7% compounded yearly for 6 years:
- \( P = 5324 \)
- \( r = 6.7\% = 0.067 \)
- \( n = 6 \)
Therefore, the correct expression to calculate the final amount is:
\[ 5324(1 + 0.067)^6 \]
Now, looking at your options, the correct expression is:
**$5,324(1+0.067)^6**
\[ A = P(1 + r)^n \]
where:
- \( A \) is the final amount,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the interest rate (as a decimal), and
- \( n \) is the number of years.
For your loan of $5,324 with a compound interest rate of 6.7% compounded yearly for 6 years:
- \( P = 5324 \)
- \( r = 6.7\% = 0.067 \)
- \( n = 6 \)
Therefore, the correct expression to calculate the final amount is:
\[ 5324(1 + 0.067)^6 \]
Now, looking at your options, the correct expression is:
**$5,324(1+0.067)^6**
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