Question

Rework parts a, b, and c assuming they are annuities due. Future value of $1,000 per year for 14 years at 12%: $ Future value of $500 per year for 7 years at 6%: $ Future value of $400 per year for 7 years at 0%:

Answer 1

The future value of an annuity due can be calculated by adjusting the formula to account for the initial payment compounding for an additional period. For the given examples, you would use the future value formula for annuities due with their respective interest rates and timelines.

Step-by-step explanation:

To calculate the future value of an annuity due, we adjust the standard future value formula to account for the fact that payments are made at the beginning of each period, which means each payment compounds for an additional period.

For example, the future value of $1,000 per year for 14 years at 12% would be:

FV = P \times \left(\frac{\left[(1 + r)^t - 1\right]}{r}\right) \times (1+r)

Where:

• FV = Future Value
• P = Payment per period ($1,000)
• r = Interest rate (12% or 0.12)
• t = Number of periods (14 years)

We'll do similar calculations for the $500 per year for 7 years at 6% annuity due, and for the $400 per year for 7 years at 0% annuity due, recognizing that at 0% interest, the future value is simply the sum of the payments.