ng a to borrow $300,000 to be repaid in a lump sum at the end of nine years. Int
ID: 425710 • Letter: N
Question
ng a to borrow $300,000 to be repaid in a lump sum at the end of nine years. Interest payments will be made on the loan at the end of each year. The company is considering the following three financing arrangements borrow the money using a fixed rate loan (FRL) that requires interest payments of 9% per year each of the first five years. At the beginning of the sixth year, the The company can borrow interest rate on the loan could change to 7%, 9%, or 11% with probabilities of 0.1, 0.25, and 0.65 the money using an adjustable rate loan (ARL) that requires interest payments of 6% at the end of can borrow the money using an ARL that requires interest payments of 4% at the end of each of the first three years. At the beginning of the fourth year, the d dinge io to, e s, er ,0% with pribablites ir 0.05, 0.30, and 0.65, respectively. At the beginnng y of 0. of the seventh year, the interest rate could decrease by 1 percentage point with a 1, increase by 1 percentage point with a probability of 0.2, or increase by 3 percentage points with a probability of 0.7 a. Create a decision tree for this problem, computing the total interest paid under each possible scenario. Option 2 Option 3 20 8 9Explanation / Answer
the principle amount is $300,000
option 1 with fixed interest rate is 9%= $300,000*0.09= $27,000, and for 9 years it is 27,000*9= $243,000
option 2= 6% for first 5 years, and next 7%, 9% and 11% with probabilities of 0.1, 0.25, and 0.65
the interest rate for second 4 years will be= 7*0.01+ 9*0.025+11*0.11= 0.07+ 0.225+7.15= 7.445
then the payment becomes= 300,000*0.06*5+ 300,000*0.07445*4= 90,000+89,340= 179,340
option 3= 4% for first 3 years= 300,000*0.04*3= 36,000
begining of 4th year, it changes as= 6* 0.05+8*0.30+ 10*0.65= 0.3+2.4+6.5= 9.2%
for next 3 years the interest rate is 9.2% and the payment is= 300,000*0.092*3= 82,800
for the last 3 years= (-1*0.01)+ (1*0.02)+ (3*0.07)= (0.01)+ .02+.0.21= 0.22 the interest rate increased by 0.22 than earlier level. the earlier year it is 9.2% and is increased by 0.22%.
now the interest rate for last 3 years is 9.22*1.22= 11.2484 (take it as 11.25%)
the payment is= 300,000*0.1125*3= 101,250
the payment for otpion 3 is= 101,250+82,800+36,000= 220,050
option 2 is the best alternative among these 3
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