Suppose you want to buy a car, you are allowed to pay the car in a series of payments over time

1) Present Value

PV = FV * 1/(1+r)ⁿ

Therefore,

10,000/(1+ 0.05)⁰ + 10,000/(1+0.05)¹ + 10,000/(1+0.05)² = 10,000+ 9523.8 + 9070.2 = $28,594

2) No. I would insist on making the three $10,000 payments because, as per Present value calculations the PV of the three payments is $ 28,594, whereas after the cash discount the total amount which I will have to pay right now is $28,700 which is greater than the previous option.
Hence, I would choose to make the three $10,000 payments.

3) When the interest rate is at 3%

10,000/(1+ 0.03)⁰ + 10,000/(1+0.03)¹ + 10,000/(1+0.03)^{2 = 10,000 + 9708.7 + 9425.9 = $29,143.6}

If the interest rate is reduced to 3% then the present value of the three payments amounts to $29,143.6, which is greater than the amount payable if a cash discount is availed which is $28,700.
Therefore, it would be wise to opt for the cash discount rather than make the three payments in this instance.