## What is A Hire Purchase Loan?

## What is an Effective Interest Rate (EIR)?

- The effective interest rate (EIR), is used to compare the annual interest between financial products. It takes into account the effects of compounding interest, which can have a significant impact on the total amount of interest paid or earned.
- The EIR is different from the nominal interest rate, which is the simple interest rate quoted on loans and investments. The nominal rate does not take into account the effects of compounding.
- The effective interest rate is derived from the loan formula:

^{-n}

- P = Monthly Repayment
- PV = Present Value (Loan amount)
- R = Rate Per Period
- N = Number of Periods

- To calculate the EIR, we need to find the interest rate (r) that makes the present value (PV) of these payments equal to the loan amount. This is a bit tricky and takes many steps to solve algebraically, but we can use a financial calculator to find the rate.
- The effective interest rate will always be higher than the nominal rate if there is more than one compounding period per year. This is because the EIR takes into account the fact that interest is being compounded, i.e., interest is earned or paid on previous interest.

## What happens if we do not calculate EIR before taking out a loan?

If you don’t calculate the Effective Interest Rate (EIR) before taking out a loan, you may underestimate the true cost of borrowing money. Here’s why:

**Misleading Interest Rates:**The nominal interest rate provided by the financial institution does not take into account the compounding periods. Therefore, it may seem lower than what you’ll actually end up paying.**Comparing Loans:**If you’re comparing loans from different institutions, one might have a lower nominal rate but compound more frequently, making it more expensive than a loan with a higher nominal rate but less frequent compounding. Without calculating the EIR, you might choose the more expensive loan.**Cost of Borrowing:**The EIR gives you a more accurate picture of the true cost of borrowing. Without it, you might not budget correctly for your repayments and could potentially end up in financial difficulty.

Remember, the EIR is a tool to help you understand the true cost of borrowing. It’s always a good idea to calculate it before taking out a loan.

# Example for Understanding

**Scenario:**Bank A offers a loan of $50,000 at a nominal interest rate of 5% per year, compounded monthly. The loan tenure is 5 years.

- P = Monthly Payment
- PV = Present Value (Loan Amount)
- r = Nominal Interest Rate
- t = Tenure (Year)

**Approach 1**does not apply. The EIR is derived from the loan formula:

^{-n}

- P = Monthly Payment
- PV = Present Value (Loan Amount)
- R = Rate Per Period
- N = Number of Periods

#### Summary

So, in both approaches, the actual amount paid over the life of the loan is the same. The difference lies in the understanding of the cost of the loan. In **Approach 1**, you might think the cost of the loan is 5% per year, but in **Approach 2**, by calculating the EIR, you realise the actual cost of the loan is approximately 9.16% per year due to the effects of monthly compounding. This could influence your decision if you were comparing this loan to others with different compounding frequencies.