Question

Paisley Motors helped out a vendor by lending them money to upgrade their supply chain. Paisley is willing to give the vendor some time before repaying the loan. The vendor will start making payments of $26,424 at the end of year 6, decreasing the payment amount by 18% each subsequent year. The vendor will make a total of 10 payments (one at the end of each year). The company is thinking of selling the loan to a third party and needs to know how much the future loan payments are worth today. Use a nominal annual interest rate of 8%, compounded monthly to make the calculation. Enter your answer as follows: 12345 Round your answer. Do not use a dollar sign ("$"), any commas (",") or a decimal point (":")

Answer 1

Effective rate = (1+0.08/12)^12 -1

= 1.0829995 -1

= 0.0829995 ~ 0.083

Present value of loan payment at EOY 5 = 26424 * [1 - (1-0.18)^10 / (1+0.083)^10] / (0.083 + 0.18)

= 26424 * [1 - (0.82)^10 / (1.083)^10] / (0.263)

= 26424 * 3.5668316

= 94249.96

Present value at EOY 0 = 94249.96 / (1+0.083)^5

= 94249.96 / (1.083)^5

= 63261.41 ~ 63261 (Nearest Dollar)