Final answer:
Using the formula for continuously compounded interest, Jaden's $200 deposit with a 12% annual interest rate will grow to approximately $299.60 in 2 years.
Step-by-step explanation:
Jaden has opened a savings account with a principal of $200.00 that earns 12% interest, compounded continuously. To calculate how much money he will have in 2 years to spend on a new bicycle, we will use the continuous compounding interest formula A = Pert, where A represents the amount of money accumulated after n years, including interest, P is the principal amount, e is the base of the natural logarithm often rounded off as approximately 2.71828, r is the annual interest rate (in decimal), and t is the time the money is invested or borrowed for, in years.
By substituting the values into the formula, we get A = 200e(0.12)(2). Calculating e(0.12)(2) will give us the factor by which the principal will grow after 2 years. After computing this, we multiply the result by the principal of $200 to find the balance A, or the final amount that Jaden will have available to spend on the bicycle.
After performing the calculations, Jaden's balance after 2 years will be A = 200e0.24, which upon calculation amounts to approximately $299.60. This indicates that Jaden will be able to spend around $299.60 on the new bike after 2 years considering the continuous compounding of interest.