To calculate the amount Braden will have in 3 years with an initial investment of $700 at an annual interest rate of 10% compounded annually, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
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).
- \(n\) is the number of years the money is invested or borrowed.
For Braden's case:
- \(P = 700\)
- \(r = 0.10\) (10% expressed as a decimal)
- \(n = 3\)
Now we can plug in the values:
\[ A = 700(1 + 0.10)^3 \] \[ A = 700(1.10)^3 \]
Calculating \(1.10^3\):
\[ 1.10^3 = 1.331 \]
Now substitute back into the formula:
\[ A = 700 \times 1.331 \] \[ A = 931.70 \]
Thus, to the nearest cent, Braden will have $931.70 in 3 years.
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