Question
Kimberly has $400 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will she have in 1 year?
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 she have in 1 year?
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 in Kimberly's account after 1 year with the given formula \( B = p(1 + r)^t \), we need to identify the values for \( p \), \( r \), and \( t \):
- \( p = 400 \) (the principal amount)
- \( r = 0.05 \) (the interest rate expressed as a decimal, which is 5% or 0.05)
- \( t = 1 \) (the time in years)
Now we can substitute these values into the formula:
\[
B = 400(1 + 0.05)^1
\]
Calculating inside the parentheses first:
\[
B = 400(1.05)^1
\]
Now evaluate \( 1.05^1 \):
\[
B = 400 \times 1.05 = 420
\]
Therefore, after 1 year, Kimberly will have **$420.00** in her account.
- \( p = 400 \) (the principal amount)
- \( r = 0.05 \) (the interest rate expressed as a decimal, which is 5% or 0.05)
- \( t = 1 \) (the time in years)
Now we can substitute these values into the formula:
\[
B = 400(1 + 0.05)^1
\]
Calculating inside the parentheses first:
\[
B = 400(1.05)^1
\]
Now evaluate \( 1.05^1 \):
\[
B = 400 \times 1.05 = 420
\]
Therefore, after 1 year, Kimberly will have **$420.00** in her account.