Question

Problem 3 B) Pierluigi is trying to get a loan for $10,000 to start a business as a financial advisor and is trying to decide between several options. (15 points) DA $10,000 loan that needs to be paid back in 6 years with a 6 % nominal annual interest rate, compounded monthly i) A $10,000 loan that needs to be paid back in 7 years, which accrues no interest during the first 2 years but has a 10% effective interest rate over the next 5, compounded monthly. Hint When solving for the annual payment consider PV-A+ATA(P/A%n) where A is the uniform annual payment Assuming that in each case he plans to make equal yearly payments for the full length of the loan: What is the amount of his yearly payment in each case? (2*5 points) Now assume that the interest rate of the market is an effective annual rate of 3%, what is the a) b) present value of the annuity payments for each option? Based on this metric, which is better? (4+1 points)

Answer 1

Answer 3 (i) :-

Year end	Remaining loan amount	Interest	Total installment
1	10000	616.78	1667+616.78=2283.78
2	8333	513.96	2180.96
3	6666	411.14	2078.14
4	4999	308.33	1975.33
5	3332	205.51	1872.51
6	1667	102.82	1769.82

Working :-

1) Yearly fixed installment = 10000/6 =1667

2) The interest rate compounding formula :-

Annual payment =Principal (1+r/n)^nt

Answer 3 (ii) :-

a) Yearly payment table :-

Year	Remaining Principal	Interest	Monthly installment
1	10000	-	1428
2	8572	-	1428
3	7145	748.17	2176.17
4	5717	598.64	2026.64
5	4289	449.11	1877.11
6	2861	299.58	1727.58
7	1428	149.53	1577.53

Working notes :-

1) The annual fixed principal payment = 10000/7=1428

2) No interest payment for first two years

b ) NPV :-

Option 1 :-

NPV = (2283.78/(1.03)¹⁾+(2180.96/(1.03)2)........(1769.82/(1.03)⁶)

=2217.26+2065.76+1901.84+1755.07+1615.35+1482.26

=11037.54

Option 2 :-

NPV =(1428/(1.03)¹)+........(1577.53/(1.03)⁷)

= 1386.40+1346.03+1991.55+1800.66+1619.32+1446.88+1282.75

=10873.59

After comparison of both NPV , option 2 is more feasible