Question
Braden has $700 in an account that earns 10% interest compounded annually.
To the nearest cent, how much will he have in 3 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.
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To the nearest cent, how much will he have in 3 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 Braden will have in 3 years with an initial amount of $700 at an interest rate of 10% compounded annually, we can use the formula:
\[
B = p(1 + r)^t
\]
Where:
- \( B \) = final balance
- \( p \) = principal (starting amount) = $700
- \( r \) = interest rate (as a decimal) = 10% = 0.10
- \( t \) = time in years = 3
Now, plug in the values:
\[
B = 700(1 + 0.10)^3
\]
\[
B = 700(1.10)^3
\]
Calculating \( (1.10)^3 \):
\[
(1.10)^3 = 1.1 \times 1.1 \times 1.1 = 1.331
\]
Now, substitute back into the formula:
\[
B = 700 \times 1.331
\]
Calculating this gives:
\[
B = 931.70
\]
Thus, to the nearest cent, Braden will have **$931.70** after 3 years.
\[
B = p(1 + r)^t
\]
Where:
- \( B \) = final balance
- \( p \) = principal (starting amount) = $700
- \( r \) = interest rate (as a decimal) = 10% = 0.10
- \( t \) = time in years = 3
Now, plug in the values:
\[
B = 700(1 + 0.10)^3
\]
\[
B = 700(1.10)^3
\]
Calculating \( (1.10)^3 \):
\[
(1.10)^3 = 1.1 \times 1.1 \times 1.1 = 1.331
\]
Now, substitute back into the formula:
\[
B = 700 \times 1.331
\]
Calculating this gives:
\[
B = 931.70
\]
Thus, to the nearest cent, Braden will have **$931.70** after 3 years.