How much will I repay in total for a $30,000 loan over 12 months with an advertised interest rate of 2.88% and an EIR of 5.84%?

To determine the total amount you need to pay for a \$30,000 loan over 12 months, we’ll consider both the advertised interest rate and the Effective Interest Rate (EIR).

Understanding the Rates

1. Advertised Interest Rate (Flat Rate): This is often a simple interest rate applied to the original principal, without considering the effects of compounding. In this case, it’s 2.88% per annum.
2. Effective Interest Rate (EIR): This rate accounts for the effects of compounding and provides a more accurate representation of the loan’s true cost. Here, it’s 5.84% per annum.

Calculations

Option 1: Using the Advertised Flat Rate

1. Calculate Total Interest: \[ \text{Total Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] \[ \text{Total Interest} = \$30,000 \times 2.88\% \times 1 = \$864 \]
2. Calculate Total Repayment Amount: \[ \text{Total Repayment} = \text{Principal} + \text{Total Interest} \] \[ \text{Total Repayment} = \$30,000 + \$864 = \$30,864 \]

Option 2: Using the Effective Interest Rate (EIR)

1. Calculate Monthly Interest Rate: \[ \text{Monthly Rate} = \left(1 + \frac{\text{Annual EIR}}{100}\right)^{\frac{1}{12}} – 1 \] \[ \text{Monthly Rate} = \left(1 + \frac{5.84}{100}\right)^{\frac{1}{12}} – 1 \approx 0.4743\% \]
2. Calculate Monthly Payment Using the Amortization Formula: \[ \text{PMT} = P \times \frac{r(1 + r)^n}{(1 + r)^n – 1} \] Where:
   • \( P = \$30,000 \)
   • \( r = 0.004743 \) (monthly rate as a decimal)
   • \( n = 12 \)

   Plugging in the values: \[ \text{PMT} = \$30,000 \times \frac{0.004743 \times (1 + 0.004743)^{12}}{(1 + 0.004743)^{12} – 1} \\ \approx \$2,580.14 \]

3. Calculate Total Repayment Amount: \[ \text{Total Repayment} = \text{Monthly Payment} \times \text{Number of Payments} \] \[ \text{Total Repayment} = \$2,580.14 \times 12 \approx \$30,961.68 \]

Option 3: Calculating Using EIR Without Amortization (Simple Compound Interest)

1. Calculate Total Repayment Amount: \[ \text{Total Repayment} = P \times \left(1 + \frac{\text{Annual EIR}}{100}\right) \] \[ \text{Total Repayment} = \$30,000 \times \left(1 + \frac{5.84}{100}\right) = \$31,752 \]

Conclusion

• Using the advertised flat rate, you’d pay a total of \$30,864.
• Using the EIR with amortized payments, you’d pay approximately \$30,961.68.
• Using the EIR with simple compound interest, the total repayment is \$31,752.

Best Estimate

Since the EIR provides a more accurate reflection of the loan’s cost, including compounding and any fees, it’s advisable to use the EIR for calculating the total repayment. Therefore, you should expect to pay approximately \$31,752 over the 12-month period.

Answer: Approximately \$31,752 is the total amount you need to pay for the \$30,000 loan over 12 months.