A store offers you a 5% discount on the cost of your purchase if you pay cash today.
Otherwise, you will be billed the full price with payment due in a quarter.
The third option is you will be billed 33% of the cost for the following three months.
1) What is the implicit borrowing rate (effective annual interest rate) being paid by customers who choose to defer payment for a quarter?
2) What is the implicit borrowing rate (effective annual interest rate) being paid by customers who choose the installment?
3) Now suppose you have to defer the payment, and the offered EAR of your credit card company is 27%, which purchase option would you prefer?
Please also show the process
Here it is assumed that the Cost of purchase is $100 and if we make upfront payment then we have to pay $95 thus loan amount for calculating effective annual interest rate = $95
1.
| Loan Amount 95 |
Annual Interest Rate 63.1579% |
Term 1 periods |
| Period | Payment | Principal Part | Interest Part | Balance |
| 1 | $100.00 | $95.00 | $5.00 | $0.00 |
2.
| Loan Amount 95 |
Annual Interest Rate 25.0901% |
Term 3 periods |
| Period | Payment | Principal Part | Interest Part | Balance |
| 1 | $33.00 | $31.01 | $1.99 | $63.99 |
| 2 | $33.00 | $31.66 | $1.34 | $32.32 |
| 3 | $33.00 | $32.32 | $0.68 | $0.00 |
3.
| Loan Amount 95 |
Annual Interest Rate 27% |
Term 3 periods |
| Period | Payment | Principal Part | Interest Part | Balance |
| 1 | $33.10 | $30.96 | $2.14 | $64.04 |
| 2 | $33.10 | $31.66 | $1.44 | $32.37 |
| 3 | $33.10 | $32.37 | $0.73 | $0.00 |
We will choose the 3rd alternative because less interest is being charged in this alternative
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