Question

What is the maximum price you would offer to pay for the promise of getting $10 per year for the next 5 years (at a 5 percent discount rate)? How does your offer price change if you get $10 per year for the next 10 years? What if you get $10 per year forever?

Answer 1

Interest rate = 5% per year

From the compound interest factor table, we obtain

(P/A, 5%, 5) = 4.329

(P/A, 5%, 10) = 7.722

(P/A, 5%, ∞) = 1/0.05 = 20

Case-1: Receive $10 per year for 5 years

Present worth of the payments received = $10 * (P/A, 5%, 5) = $10 * 4.329 = $43.29

Therefore, the maximum price you should offer is $43.29

Case-2: Receive $10 per year for 10 years

Present worth of the payments received = $10 * (P/A, 5%, 10) = $10 * 7.722 = $77.22

Therefore, the maximum price you should offer is $77.22

Case-2: Receive $10 per year forever

Present worth of the payments received = $10 * (P/A, 5%, ∞) = $10 * 20 = $200

Therefore, the maximum price you should offer is $200