Final answer:
Simon must deposit approximately $710.67 as the initial principal amount in a savings account that earns 4% interest compounded monthly to have $800 in 3 years to buy the bicycle.
Step-by-step explanation:
To determine how much Simon must deposit as principal to have $800 in 3 years in a savings account that earns 4% interest compounded monthly, we need to use the compound interest formula given as A = P(1 + r/n)^(nt), 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 times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.
For Simon's case, A will be $800, r will be 0.04 (since 4% as a decimal is 0.04), n will be 12 (since interest is compounded monthly), and t will be 3 (since he wants to buy the bicycle in 3 years).
First, we need to rearrange the formula to solve for P: P = A / [(1 + r/n)^(nt)]. Plugging in the values, we get P = $800 / [(1 + 0.04/12)^(12*3)]. Calculating the denominator, we get (1 + 0.0033333)^(36) which is approximately 1.12624, so P = $800 / 1.12624 = $710.67.
Therefore, Simon needs to deposit approximately $710.67 as principal to have $800 in 3 years with a 4% interest rate compounded monthly.