Question

Problem 1 Greg borrowed $100,000 to purchase a house. He agreed to repay the loan with equal monthly payments over a 30 year period at a nominal annual rate of 6 percent. a. What would be his monthly payment? b. What is the effective annual interest rate on the loan? c. Consider a closing fees of $2,000 on the loan. If he chooses to finance the closing costs, then what would be his monthly payment? d. What is the effective annual interest rate on the loan if he chooses to finance the closing costs? Problem 2 Excavator Useful Life Initial Investment Annual Operating Cost Salvage Value A B C 4 yrs 5 yrs 6 yrs $15,500 $20,250 $30,750 $8,750 $5,850 $3,175 $2,500 $3,000 $3,250 A construction engineer has been asked to recommend an excavator for ac- quisition. Three alternatives have been identified, having the characteristics shown in the table above. A MARR of 12 percent is used. a. Find the best alternative using the annual cost method. b. Find the present worth of each of the acquisitions. Can you use the present worth values to compare the alternatives? Explain your answer.

Please don’t use Excel and do all the parts of the questions. Show your work!!!

Answer 1

Problem 1: The formula to calculate the present value of an annuity is shown below: 1-(1+7) Present value = C- Present value = c 14 (47) Here, The equal period payment is denoted as C. The periodic interest rate is r. The number of period payments is n. 16% The annual interest rate is 6%. Therefore, its monthly counterpart will be 0.5% per month ( 12 Substitute the given values in the formula above to calculate the monthly payment as follows: $100,000= 1-(1+0.5%) 30x22) 7 0.5% $100,000 166.7916144 = $599.55 Therefore, the monthly payment required is $599.55. Calculate the effective annual interest rate as follows: Annual rate Effective annual rate = 1+- 12 12 60, 6 % 12 = 0.06168 Therefore, the effective annual interest rate is 6.168%. If a closing fee of $2,000 is also considered, the effective loan amount would equal $102,000. Substitute this value in the present value of annuity formula to calculate the monthly payment as shown below: 1-(1+0.5%) -30~12) $102,000=C 0.5% $102,000 166.7916144 = $611.54 Therefore, the monthly payment in this case is $611.54. d. The effective annual interest rate would still be 6.168%. This is because only the loan amount is changing but the effective interest being paid on that is still the same.