1) (25 points) You need to borrow $10,000 now to pay your tuition bill You would
ID: 2621154 • Letter: 1
Question
1) (25 points) You need to borrow $10,000 now to pay your tuition bill You would like to pay it back as a single lump sum amount in 3 years from now. Bank A charges l 5% per year compounded monthly on cducation loans. Bank B charges 12% per year compounded daily on education loans, but has a 10% (of the original loan amount) handling fee that needs to be paid upfront. However, the bank is willing to allow you to roll the handling fee into the loan amount; ie., the bank will loan you the original amount plus the handling fee. Both banks have agreed to a single lump sum payment at the end of three years. What would you do? Show all workExplanation / Answer
For Bank A
Annual Rate on loan = 15% Compounded Monthly
Effective annual rate = [(1 + 15% / 12) ^ 12] - 1
= 1.1608 - 1
= 16.08%
Effective annual rate in Bank A is 16.08%.
Total Lumpsum amount need to pay at year 3 = $10,000 × (1 + 16.08%) ^ 3
= $10,000 × 1.563944
= $15,639.44.
Total Lump sum amount need to pay at year 3 is $15,639.44.
For Bank B
Annual Rate on loan = 12% Compounded daily
Effective annual rate = [(1 + 12% / 12) ^ 12] - 1
= 1.1268 - 1
= 12.68%
Effective annual rate in Bank B is 12.68%.
Bank Charge 10% Handling fee.
So total amount need to borrow = $10,000 × (1 + 10%)
= $11,000
Total amount need to borrow is $11,000.
Total Lumpsum amount need to pay at year 3 = $11,000 × (1 + 12.68%) ^ 3
= $11,000 × 1.430769
= $15,738.46.
Total Lump sum amount need to pay at year 3 is $15,738.46.
SInce, Total Lump Sum amount need to pay in year 3 in bank A is lower than Bank B. So you should choose bank A for student loan.
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