A firm has decided to borrow $500,000 on a 10% add-on basis, payable in 8 end-of-month installments. What would the nominal annual percentage rate on the loan be.
To find the nominal annual percentage rate (APR) on the loan, we need to consider the add-on interest rate and the repayment terms.
Here's how you can calculate the nominal APR:
Step 1: Calculate the total interest paid on the loan.
- The loan amount is $500,000.
- The add-on interest rate is 10%.
- Multiply the loan amount by the add-on interest rate: 500,000 * 0.10 = $50,000.
- The total interest paid on the loan is $50,000.
Step 2: Calculate the total repayments.
- The loan is payable in 8 end-of-month installments, which means 8 payments in total.
- Each payment is equal.
- Divide the total loan amount plus interest by the number of payments: (500,000 + 50,000) / 8 = $62,500.
- The total repayments are $62,500.
Step 3: Convert the repayment period to a year.
- Since each monthly payment is made at the end of the month, there are 12 months in a year.
- Multiply the number of payments by 12: 8 * 12 = 96 months.
Step 4: Calculate the nominal APR.
- Divide the total interest paid by the total repayments and multiply by 100 to get the percentage: (50,000 / 500,000) * 100 = 10%.
- Divide the nominal APR by the number of payments per year: 10% / 96 = 0.104167.
Therefore, the nominal annual percentage rate (APR) on the loan would be approximately 10.42%.