What is the present value (PV) of an annuity due with 5 payments of \$2 each, assuming a discount rate of 10% per period?

• A. \$9.00
• B. \$8.21
• C. \$7.57
• D. \$7.91

Answer: (D)

Verified step by step guidance

1. Understand the concept of an annuity due: An annuity due is a series of equal payments made at the beginning of each period. The present value (PV) of an annuity due is calculated by discounting each payment back to its present value using the given discount rate.
2. Identify the key variables: The number of payments (n) is 5, the payment amount (PMT) is \$2, and the discount rate (r) is 10% or 0.10 per period.
3. Use the formula for the present value of an annuity due: \( PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r) \). The extra \( (1 + r) \) factor accounts for the fact that payments are made at the beginning of each period.
4. Substitute the values into the formula: \( PV = 2 \times \left( \frac{1 - (1 + 0.10)^{-5}}{0.10} \right) \times (1 + 0.10) \). Break this into smaller steps for calculation: first calculate \( (1 + r)^{-n} \), then \( 1 - (1 + r)^{-n} \), then divide by \( r \), and finally multiply by \( PMT \) and \( (1 + r) \).
5. Perform the calculations step by step to arrive at the present value. Ensure that each intermediate step is clear and accurate, and remember that the final result will be the present value of the annuity due.