Your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making 10 yearly payments with the ﬁrst payment being made at the end of this
Year. If the payments are to grow by 10% each year and the appropriate discount rate is 12%, how
Much will your neighbour have to pay at the end of the ﬁrst year?

Question

Quizplus · Accepted Answer

The correct answer is A. The present value of the payments is $10,000. The first payment is $10,000 * 0.1 = $1,000. The discount factor for the first year is 1 / (1 + 0.12) = 0.8929. The present value of the first payment is $1,000 * 0.8929 = $892.90. The future value of the first payment is $892.90 * (1 + 0.1) = $982.19. The present value of the remaining payments is $10,000 - $892.90 = $9,107.10. The discount factor for the second year is 1 / (1 + 0.12)^2 = 0.7972. The present value of the remaining payments is $9,107.10 * 0.7972 = $7,250.00. The future value of the remaining payments is $7,250.00 * (1 + 0.1) = $8,025.00. The total future value of the payments is $982.19 + $8,025.00 = $9,007.19. The neighbour will have to pay $9,007.19 - $10,000 = $1,007.19 at the end of the first year.

Your Neighbour Makes You the Following Offer