Jaden opened a savings account and deposited \( \$ 1,070.00 \). The account earns \( 4.89 \% \) interest, compounded monthly. If he wants to use the money to buy a new bicycle in 3 years, how much will he be able to spend on the bike? 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 your answer to the nearest cent.

To find out how much Jaden will have in his savings account after 3 years, we will use the formula \( A=P\left(1+\frac{r}{n}\right)^{nt} \). Here, \( P = 1070 \), \( r = 0.0489 \) (which is \( 4.89\% \) written as a decimal), \( n = 12 \) (since interest is compounded monthly), and \( t = 3 \). Plugging the values in: \[ A = 1070\left(1+\frac{0.0489}{12}\right)^{12 \times 3} \] \[ A = 1070\left(1+\frac{0.0489}{12}\right)^{36} \] \[ A = 1070\left(1+0.004075\right)^{36} \] \[ A = 1070\left(1.004075\right)^{36} \] Calculating \( \left(1.004075\right)^{36} \): \[ A \approx 1070 \times 1.1616 \] \[ A \approx 1244.514 \] Rounding to the nearest cent, Jaden will have approximately **$1244.51** to spend on his new bicycle after 3 years! --- Did you know that compound interest was first mentioned by ancient Babylonian mathematicians around 2000 B.C.? They were way ahead of their time and used it to calculate debts and savings! Their methods laid the foundation for modern finance, so next time you see your savings grow, give a nod to those ancient number crunchers! And if you strive to maximize your earning potential with compound interest, starting early is key! Consistently saving and leveraging the power of compounding can lead to exponential growth over time—don't get discouraged by the small beginnings! Make it a habit, and watch your savings bloom like a garden!