Final answer:
The amount of $1000 compounded after 10 years varies based on the compounding frequency. Scenario (a) is compounded annually at 6%, (b) quarterly at 6%, and (c) continuously at 6%. The calculation uses different formulas for each scenario, considering the frequency of compounding.
Step-by-step explanation:
Compounded Interest Calculations
To determine the amount of $1000 compounded interest over 10 years, three different scenarios are considered.
The formulas for each type of compounding will vary based on the compounding frequency. The following outlines the calculations for each situation as requested:
(a) Annually at 6%: The formula used is A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
For annual compounding, n is 1. So, A = 1000 (1 + 0.06/1)^(1*10).
(b) Quarterly at 6%: Using the same formula but changing n to 4 since interest is compounded quarterly, the calculation is A = 1000 (1 + 0.06/4)^(4*10).
(c) Continuously at 6%: For continuous compounding, the formula is different: A = Pe^(rt), where e is the base of the natural logarithm, roughly equal to 2.71828. Thus, A = 1000 * e^(0.06*10).
By computing these formulas, you can find the total amount of $1000 compounded at different rates and frequencies after 10 years. Please note that in actual financial scenarios, taxes and fees would potentially affect the final amount.