Question
Suzie has $9,126 in an account. The interest rate is 10% compounded annually.
To the nearest cent, how much will she have in 5 years?
$
To the nearest cent, how much will she have in 5 years?
$
Answers
GPT-4o mini
To calculate the future value of an investment with compound interest, you can use the formula:
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
For Suzie's account:
- \( P = 9,126 \)
- \( r = 0.10 \) (10% as a decimal)
- \( t = 5 \)
Now plug in the values:
\[
A = 9,126(1 + 0.10)^5
\]
First, calculate \( (1 + 0.10)^5 \):
\[
1.10^5 \approx 1.61051
\]
Now substitute this value back into the equation:
\[
A \approx 9,126 \times 1.61051
\]
Calculate this:
\[
A \approx 14,703.57
\]
So to the nearest cent, Suzie will have approximately **$14,703.57** in 5 years.
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
For Suzie's account:
- \( P = 9,126 \)
- \( r = 0.10 \) (10% as a decimal)
- \( t = 5 \)
Now plug in the values:
\[
A = 9,126(1 + 0.10)^5
\]
First, calculate \( (1 + 0.10)^5 \):
\[
1.10^5 \approx 1.61051
\]
Now substitute this value back into the equation:
\[
A \approx 9,126 \times 1.61051
\]
Calculate this:
\[
A \approx 14,703.57
\]
So to the nearest cent, Suzie will have approximately **$14,703.57** in 5 years.