Question

You are considering the purchase of a successful coffee shop near campus for $107413 because it has the potential fund your living expenses while in college. You have $7413 in cash, but need to borrow the balance. For each of the two options you are considering, calculate the value of lump sum payment, F, due at end of five years and the total interest cost, E. Which of these options do you prefer? Take a loan from an older family member at 10%/year simple interest to be paid in full at the end of five years. Pursue a Small Business Loan from local bank with 8% APR compounded monthly, and no payments are due until the end of five years. However, you will need to have your family co‐sign to qualify.   

Answer 1

Ans.
Loan amount = balance amount = 107413 - 7413 = $100000

Option when loan is taken from a family member at a simple interest of 10%

Total Amount paid after 5 years, F = Loan + Simple interest on loan

=> F = 100000 + 100000*0.10*5

=> F = $150000

Option when loan is taken from a bank,

As the interest rate is componded monthly,

So, number of periods = 5*12 = 60 months

Interest rate per month = 8/12 = 0.67%

Thus, the loan amount repaid = 100000*(1+0.0067)^60

=> F = $148984.6

So, bank should be taken from the bank as the lumpsum amount to paid to the bank after 5 years is less than what needs to paid to the relative if loan was taken from him

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