What is A Hire Purchase Loan?
A hire purchase loan is a type of monthly instalment plan you can use to purchase an asset, which will require the buyer to make an initial down payment and pay the remaining capital plus the interest repayment. The rest of the amount will be incurred with interest, interest rate is provided and will be calculated using effective interest rate
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:
P
=
r(PV)
1 - (1+r)-n
Where:
- 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
Consider a scenario involving one bank but two different approaches to understanding the loan: one with the EIR and one without.
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.
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.
Approach 1: Not considering the Effective Interest Rate (EIR)
Approach 2: Considering the Effective Interest Rate (EIR)
Approach 1: Not considering the Effective Interest Rate (EIR)
You decide to simply focus on the nominal interest rate. The monthly payment is:
Where:
P
=
PVrt+PV
12t
- P = Monthly Payment
- PV = Present Value (Loan Amount)
- r = Nominal Interest Rate
- t = Tenure (Year)
The monthly payment comes out to be approximately $1042.
Over 5 years, you would pay $1042 * 12 * 5 = $62,520 in total.
The total interest paid would be $62,520 – $50,000 = $12,520.
Approach 2: Considering the Effective Interest Rate (EIR)
This time, you decide to calculate the EIR to understand the true cost of the loan as it takes the compounded period into consideration when calculating the interest which Approach 1 does not apply. The EIR is derived from the loan formula:
Where:
P
=
r(PV)
1 – (1+r) -n
- P = Monthly Payment
- 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 like SQL Professional Hire Purchase Installment Calculator
(Flat to Effective Interest Rate Calculator) to find the rate.
The EIR comes out to be approximately 9.16%.
Now, if you calculate the monthly payments using the EIR as the interest rate, you’ll get a more accurate picture of the true cost of the loan. However, it’s important to note that the EIR doesn’t change the actual monthly payments or the total amount paid over the life of the loan. It’s a tool for understanding and comparing the true cost of loans.
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.
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