Question
Aiden has $6,000 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much will he have in 5 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
To the nearest cent, how much will he have in 5 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
GPT-4o mini
To calculate the balance \( B \) in Aiden's account after 5 years using the formula \( B = p(1 + r)^t \), we can substitute the given values:
- \( p = 6000 \) (the principal amount)
- \( r = 0.05 \) (the interest rate as a decimal)
- \( t = 5 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 6000(1 + 0.05)^5
\]
First, calculate \( (1 + 0.05) \):
\[
1 + 0.05 = 1.05
\]
Next, raise \( 1.05 \) to the power of 5:
\[
1.05^5 \approx 1.2762815625
\]
Now, multiply this result by the principal:
\[
B = 6000 \times 1.2762815625 \approx 7657.689375
\]
Finally, round this result to the nearest cent:
\[
B \approx 7657.69
\]
Thus, the amount Aiden will have in his account after 5 years is approximately **$7657.69**.
- \( p = 6000 \) (the principal amount)
- \( r = 0.05 \) (the interest rate as a decimal)
- \( t = 5 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 6000(1 + 0.05)^5
\]
First, calculate \( (1 + 0.05) \):
\[
1 + 0.05 = 1.05
\]
Next, raise \( 1.05 \) to the power of 5:
\[
1.05^5 \approx 1.2762815625
\]
Now, multiply this result by the principal:
\[
B = 6000 \times 1.2762815625 \approx 7657.689375
\]
Finally, round this result to the nearest cent:
\[
B \approx 7657.69
\]
Thus, the amount Aiden will have in his account after 5 years is approximately **$7657.69**.