Your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making yearly payments with the ﬁrst payment being for $1,000 at the end of this
Year. The payments will grow by 10% every year thereafter. If the appropriate discount rate is 12%,
How long will it take for your neighbour to repay the loan?

Question

Quizplus · Accepted Answer

The present value of the payments is equal to the amount of the loan. The present value of the payments can be calculated using the formula for the present value of an annuity:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the paymentsPMT is the amount of each paymentr is the discount raten is the number of paymentsIn this case, the amount of each payment is $1,000, the discount rate is 12%, and the number of payments is unknown. We can solve for the number of payments by setting the present value of the payments equal to the amount of the loan:$10,000 = $1,000 * [1 - (1 + 0.12)^-n] / 0.12Solving for n, we get:n = 12.38 yearsTherefore, it will take the neighbor 12.38 years to repay the loan.

Your Neighbour Makes You the Following Offer