Should You Settle Your Car Loan Early? A Smart Financial Analysis Using the Rule of 78

Car Hire Purchase Loan Settlement Analysis

Introduction to Hire Purchase Loan Calculation

A hire purchase (HP) loan is a financing method commonly used for vehicle purchases. It is structured such that the total interest is calculated upfront and spread over the tenure of the loan. The Rule of 78, also known as the sum-of-digits method, is used to allocate interest payments across the loan period, meaning that more interest is paid in the earlier months of the loan.

Understanding the Rule of 78

The Rule of 78 determines how interest is distributed across the tenure by assigning decreasing weights to each month's interest payment. The sum of digits for a given number of months (N) is calculated using the formula:

$\text{Sum of Digits} = \frac{N (N+1)}{2}$

For example, for a 3-year loan (36 months):

$\text{Sum of Digits} = \frac{36 \times 37}{2} = 666$

Loan Calculation Breakdown

Given Loan Details:

• Principal (P) = $ 27,000
• Interest Rate (r) = 4.1% per annum
• Loan Tenure (T) = 3 years (36 months)

Term Charges Calculation:

$\text{Term Charges} = P \times r \times T$

$= 27000 \times 0.041 \times 3 = 3321$

Monthly Installment Calculation:

$\text{Monthly Installment} = \frac{P + \text{Term Charges}}{T \times 12}$

$= \frac{27000 + 3321}{36} = 842.25$

Early Loan Settlement After 16 Payments

If the borrower decides to settle the loan after making 16 payments, the remaining outstanding balance is calculated as follows:

Rebate Calculation:

The rebate on interest is calculated using:

$\text{Rebate} = \frac{(N-n)(N-n+1) \times \text{Term Charges}}{N(N+1)}$

$= \frac{(36-16)(36-16+1) \times 3321}{36 \times 37}$

$= \frac{20 \times 21 \times 3321}{36 \times 37} = 1047.16$

Outstanding Installments Calculation:

$\text{Outstanding Installments} = (N - n) \times \text{Monthly Installment}$

$= (36 - 16) \times 842.25 = 16845$

Redemption Sum (Settlement Amount):

$\text{Redemption Sum} = \text{Outstanding Installments} - \text{Rebate}$

$= 16845 - 1047.16 = 15797.84$

Interest Savings and Effective Interest Rate Analysis

Interest Savings Calculation:

$\text{Interest Savings} = \text{Total Payment in Old Plan} - \text{Total Payment in Settled Plan}$

$= (842.25 \times 36) - (15797.84 + (16 \times 842.25))$

$= 30321 - 29273.84 = 1047.16$

Effective Interest Rate:

The effective interest rate (EIR) can be computed using the Excel's RATE function:

$\text{EIR (Old Plan)} = 12 \times RATE(36, -842.25, 27000, 0, 0, 0.15)$

$= 7.692\% \text{ per annum}$

Alternatively, using the internal rate of return (IRR) from cash flow:

$\text{EIR (Old Plan)} = 7.515\% \text{ per annum}$

Decision Analysis: Is Early Settlement Worth It?

To determine whether early settlement is financially beneficial, we compare the interest savings against an alternative investment option, such as a fixed deposit (FD) at 3% p.a.:

• Interest Savings from Settlement = $ 1047.16

• Potential Return from FD (assuming the $ 15,806.84 is placed in FD at 3% p.a.)

  $\text{Future Value} = 15797.84 \times (1.03)$

  $= 16271.76$

Since the effective interest rate of the loan (7.515%) is higher than the FD rate (3%), settling the loan early provides financial benefits by reducing the overall interest paid.

Conclusion

Based on the calculations, early settlement of the hire purchase loan after the 16th payment leads to savings of $ 1047.16 in interest. Given that the effective interest rate of the loan (7.515%) is significantly higher than the alternative FD investment rate (3%), it is financially advantageous to settle the loan early. Thus, executing the early settlement is a prudent financial decision.