To find the effective rate for the proceeds of $13,214 from a 147-day loan with a discount of $512 paid to the bank, follow these steps:
1. Calculate the proceeds after the discount:
Proceeds = Loan Amount - Discount
Proceeds = $13,214 - $512
Proceeds = $12,702
2. Determine the interest paid on the loan:
Interest = Proceeds - Loan Amount
Interest = $12,702 - $13,214
Interest = -$512 (negative because the bank received more money upfront due to the discount)
3. Calculate the interest rate for 147 days:
Interest Rate = (Interest / Loan Amount) * (365 / Days)
Interest Rate = (-$512 / $13,214) * (365 / 147)
Interest Rate = -0.0386
4. Convert the interest rate to a positive value:
Effective Rate = |Interest Rate|
Effective Rate = 0.0386 or approximately 3.86%
Therefore, the effective rate for the proceeds of $13,214 from a 147-day loan with a $512 discount paid to the bank is approximately 3.86%.
