Final answer:
To calculate the equivalent future value of a series of cash flows at a 6% compounded annual interest rate by the end of the sixth year, each cash flow needs to be compounded individually for the number of years remaining until the sixth year, and then all the calculated future values should be summed up.
Step-by-step explanation:
The question asks to calculate the equivalent single sum of money at the end of the sixth year that would be equivalent to a series of cash flows when compounded annually at an interest rate of 6%. To find this, each cash flow must be compounded to the sixth year and then summed up to get the total future value. The formula to calculate the future value of each cash flow is FV = PV (1 + r)ⁿ, where FV is the future value, PV is the present value or the cash flow amount, r is the annual interest rate, and n is the number of years until the sixth year.
To apply the formula, we calculate the future value of each cash flow from the end of each year to the end of the sixth year:
- Cash flow at EOY 1: $12,000 compounded for 5 years
- Cash flow at EOY 2: $11,000 compounded for 4 years
- Cash flow at EOY 3: $10,000 compounded for 3 years
- Cash flow at EOY 4: $9,000 compounded for 2 years
- Cash flow at EOY 5: $8,000 compounded for 1 year
- Cash flow at EOY 6: $7,000 compounded for 0 years (it is already in the sixth year)
Each cash flow is then compounded individually based on the formula and summed to calculate the total future value at the end of year 6. It is important to correctly calculate the compound interest impact as it makes a significant difference compared to simple interest, especially over longer periods of time and with larger sums of money.