Question
Polly has $10 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will she have in 2 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 she have in 2 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 find out how much Polly will have in her account after 2 years with an initial amount of $10, an interest rate of 5% (expressed as a decimal, which is 0.05), and 2 years of compounding, we can use the formula:
\[
B = p(1 + r)^t
\]
Here, we have:
- \( p = 10 \) (the principal amount)
- \( r = 0.05 \) (the interest rate)
- \( t = 2 \) (the number of years)
Now, substituting these values into the formula:
\[
B = 10(1 + 0.05)^2
\]
Calculating \( 1 + 0.05 \):
\[
1 + 0.05 = 1.05
\]
Now raising \( 1.05 \) to the power of \( 2 \):
\[
(1.05)^2 = 1.1025
\]
Now, multiplying by the principal amount:
\[
B = 10 \times 1.1025 = 11.025
\]
To find the amount to the nearest cent:
\[
B \approx 11.03
\]
Therefore, Polly will have approximately **$11.03** in her account after 2 years.
\[
B = p(1 + r)^t
\]
Here, we have:
- \( p = 10 \) (the principal amount)
- \( r = 0.05 \) (the interest rate)
- \( t = 2 \) (the number of years)
Now, substituting these values into the formula:
\[
B = 10(1 + 0.05)^2
\]
Calculating \( 1 + 0.05 \):
\[
1 + 0.05 = 1.05
\]
Now raising \( 1.05 \) to the power of \( 2 \):
\[
(1.05)^2 = 1.1025
\]
Now, multiplying by the principal amount:
\[
B = 10 \times 1.1025 = 11.025
\]
To find the amount to the nearest cent:
\[
B \approx 11.03
\]
Therefore, Polly will have approximately **$11.03** in her account after 2 years.