Question
Kenny has $500 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will he earn 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 interest will he earn 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 interest earned by Kenny in 1 year using the formula \( B = p(1 + r)^t \), we need to identify the values for \( p \), \( r \), and \( t \):
- \( p = 500 \) (the principal amount)
- \( r = 0.05 \) (the interest rate as a decimal, since 5% = 0.05)
- \( t = 1 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 500(1 + 0.05)^1
\]
Calculating step-by-step:
1. Calculate \( 1 + r \):
\[
1 + 0.05 = 1.05
\]
2. Calculate \( (1.05)^1 \):
\[
(1.05)^1 = 1.05
\]
3. Now multiply by the principal:
\[
B = 500 \times 1.05 = 525
\]
Now we find the interest earned:
Interest \( = B - p \):
\[
Interest = 525 - 500 = 25
\]
To the nearest cent, the amount of interest Kenny will earn in 1 year is **$25.00**.
- \( p = 500 \) (the principal amount)
- \( r = 0.05 \) (the interest rate as a decimal, since 5% = 0.05)
- \( t = 1 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 500(1 + 0.05)^1
\]
Calculating step-by-step:
1. Calculate \( 1 + r \):
\[
1 + 0.05 = 1.05
\]
2. Calculate \( (1.05)^1 \):
\[
(1.05)^1 = 1.05
\]
3. Now multiply by the principal:
\[
B = 500 \times 1.05 = 525
\]
Now we find the interest earned:
Interest \( = B - p \):
\[
Interest = 525 - 500 = 25
\]
To the nearest cent, the amount of interest Kenny will earn in 1 year is **$25.00**.