Final answer:
To find the present value of an annuity due with 12 payments of $6,000 at a 6.6% discount rate, adjust the present value of an ordinary annuity formula, then multiply by the payment amount, and round the result to two decimal places.
Step-by-step explanation:
To calculate the present value of an annuity due with 12 annual payments of $6,000 and a cost of capital at 6.6%, we must adjust the typical present value formula for an ordinary annuity to reflect the fact that payments are made at the beginning of each period. The formula for the present value of an annuity due is PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r), where Pmt is the payment amount, r is the periodic interest rate, and n is the number of periods. Given that our interest rate is 6.6% (or 0.066) and we have 12 payments:
- Determine the discount rate per period (r): 0.066
- Calculate the present value factor for an ordinary annuity: (1 - (1 + 0.066)^-12) / 0.066
- Adjust the present value factor for an annuity due by multiplying by (1 + 0.066)
- Multiply this adjusted factor by the payment amount ($6,000)
After completing the calculations, round off the final result to two decimal places as requested.