Oscar opened a savings account and deposited \( \$ 313.00 \) as principal. The account earns \( 12.44 \% \) interest, compounded quarterly. What is the balance after 3 years? Use the formula \( A=P\left(1+\frac{r}{n}\right)^{n t} \), where \( A \) is the balance (final amount), \( P \) is the principal (starting amount), \( r \) is the interest rate expressed as a decimal, \( n \) is the number of times per year that the interest is compounded, and \( t \) is the time in years. Round vour answer to the nearest cent.

To find the balance after 3 years, we need to plug the values into the formula \( A=P\left(1+\frac{r}{n}\right)^{n t} \). Here, \( P = 313.00 \), \( r = 0.1244 \), \( n = 4 \) (since interest is compounded quarterly), and \( t = 3 \). Using the formula: \[ A = 313\left(1+\frac{0.1244}{4}\right)^{4 \times 3} \] Calculating \( \frac{0.1244}{4} = 0.0311 \), thus: \[ A = 313\left(1 + 0.0311\right)^{12} \] This leads to: \[ A = 313\left(1.0311\right)^{12} \] Calculating \( (1.0311)^{12} \approx 1.432364654 \): \[ A \approx 313 \times 1.432364654 \approx 448.31 \] So after rounding to the nearest cent, the balance after 3 years is approximately \( \$ 448.31 \). Isn't it fascinating to see how money can grow over time? By just letting your savings sit in a good interest-bearing account, you can earn money on top of your initial deposit! When it comes to understanding this concept, it’s crucial to regularly check and understand the details of your financial accounts. Many people overlook the compounding effect or forget to factor in how frequently interest is applied, which can lead to missed opportunities in maximizing their savings. So, keep your eye on those compounding interests!