Question
Bernie deposited $2,000 in an account earning 10% interest 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 how much Bernie will have in 5 years, we will use the formula
\[
B = p(1 + r)^t
\]
Where:
- \( B \) is the balance after time \( t \)
- \( p \) is the principal amount (the initial deposit)
- \( r \) is the annual interest rate (expressed as a decimal)
- \( t \) is the time in years
Given:
- \( p = 2000 \)
- \( r = 10\% = 0.10 \)
- \( t = 5 \)
Now, we can substitute these values into the formula:
\[
B = 2000(1 + 0.10)^5
\]
\[
B = 2000(1.10)^5
\]
Now, we calculate \( (1.10)^5 \):
\[
(1.10)^5 = 1.61051
\]
Now we can calculate \( B \):
\[
B = 2000 \times 1.61051
\]
\[
B = 3221.02
\]
Thus, to the nearest cent, Bernie will have **$3,221.02** in the account after 5 years.
\[
B = p(1 + r)^t
\]
Where:
- \( B \) is the balance after time \( t \)
- \( p \) is the principal amount (the initial deposit)
- \( r \) is the annual interest rate (expressed as a decimal)
- \( t \) is the time in years
Given:
- \( p = 2000 \)
- \( r = 10\% = 0.10 \)
- \( t = 5 \)
Now, we can substitute these values into the formula:
\[
B = 2000(1 + 0.10)^5
\]
\[
B = 2000(1.10)^5
\]
Now, we calculate \( (1.10)^5 \):
\[
(1.10)^5 = 1.61051
\]
Now we can calculate \( B \):
\[
B = 2000 \times 1.61051
\]
\[
B = 3221.02
\]
Thus, to the nearest cent, Bernie will have **$3,221.02** in the account after 5 years.