Explanation:

The present value (PV) of the future lump sum payment of $500,000 in 15 years is calculated as: $PV = FV \times (1 + r)^{-N} = 500,000 \times (1 + 0.04)^{-15} = 277,632.25$

The 10 annual payments form an annuity due (since payments start today). The PV of an annuity due is equivalent to the PV of an ordinary annuity with 9 payments plus the first payment: $PV = A + A \left[ \frac{1 - (1 + r)^{-9}}{r} \right] = A \left(1 + \frac{1 - (1 + 0.04)^{-9}}{0.04}\right) = 8.4353A$

Setting the PV of the annuity equal to the PV of the lump sum: $8.4353A = 277,632.25$ Solving for $A$: $A = \frac{277,632.25}{8.4353} \approx 32,913$

Calculator steps (BGN mode):

• N = 10, I/Y = 4, PV = 277,632.25, solve for PMT = 32,913.

Why other options are incorrect:

• B: Assumes an ordinary annuity, leading to a higher PV and incorrect payment.
• C: Incorrectly assumes the lump sum is received in 10 years, overestimating the PV and payment.