Question
7800 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 29 years, to the nearest cent?
Answers
Answered by
GPT-4o mini
To calculate the amount in the account after 29 years with an annual interest rate of 6.5%, we'll 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.
In your case:
- \( P = 7800 \)
- \( r = 6.5\% = 0.065 \)
- \( t = 29 \)
Plugging in these values, we get:
\[
A = 7800(1 + 0.065)^{29}
\]
Calculating \( 1 + 0.065 \):
\[
1 + 0.065 = 1.065
\]
Now, raise \( 1.065 \) to the power of 29:
\[
1.065^{29} \approx 6.291197
\]
Now multiply this by the principal:
\[
A \approx 7800 \times 6.291197 \approx 49032.13
\]
Rounding to the nearest cent, the amount that will be in the account after 29 years is approximately:
\[
\boxed{49032.13}
\]
\[
A = P(1 + r)^t
\]
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.
In your case:
- \( P = 7800 \)
- \( r = 6.5\% = 0.065 \)
- \( t = 29 \)
Plugging in these values, we get:
\[
A = 7800(1 + 0.065)^{29}
\]
Calculating \( 1 + 0.065 \):
\[
1 + 0.065 = 1.065
\]
Now, raise \( 1.065 \) to the power of 29:
\[
1.065^{29} \approx 6.291197
\]
Now multiply this by the principal:
\[
A \approx 7800 \times 6.291197 \approx 49032.13
\]
Rounding to the nearest cent, the amount that will be in the account after 29 years is approximately:
\[
\boxed{49032.13}
\]
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