Final answer:
The future value of ordinary annuities and annuities due are calculated using specific formulas. For ordinary annuities, the payment per period is multiplied by a factor based on the interest rate and the number of periods. When reworking for annuities due, the ordinary annuity is calculated first and then adjusted for the extra compounding.
Step-by-step explanation:
To find the future value of these annuities, we use the future value formula for an annuity: FV = Pmt * [((1 + r)^n - 1) / r], where FV is the future value, Pmt is the payment per period, r is the interest rate per period, and n is the number of periods.
Ordinary Annuities:
Future value of $500 per year for 6 years at 8%: FV = $500 * [((1 + 0.08)^6 - 1) / 0.08] = $500 * [((1.08)^6 - 1) / 0.08]
Future value of $250 per year for 3 years at 4%: FV = $250 * [((1 + 0.04)^3 - 1) / 0.04] = $250 * [((1.04)^3 - 1) / 0.04]
Future value of $1,000 per year for 2 years at 0%: FV = $1,000 * 2 (since there's no interest, it's just the sum of the payments)
Annuities Due:
Future value of $500 per year for 6 years at 8% as an annuity due: We calculate the ordinary annuity as before and multiply by (1 + r) to account for the extra period of compounding
Future value of $250 per year for 3 years at 4% as an annuity due: Follow the same process as before
Future value of $1,000 per year for 2 years at 0% as an annuity due: Takes the sum and adds the extra year's payment upfront
Note: Precise numerical solutions are not provided here as the calculations for the annuity due involve using the previously calculated ordinary annuity values, and then adjusting for the extra compounding period.