Loan Repayment Comparison With Fees
Sam needs $12,000 for a car. Dealer finance offers 7.2% per annum simple interest over 4 years, with a $300 establishment fee added to the amount borrowed. The bank offers a reducing-balance loan at 6.5% per annum compounding monthly over 4 years, with a $250 application fee paid upfront (not borrowed). Sam can afford about $300 per month. He wants the lower total cost but also wants to know which loan is riskier if he misses a payment.
1. Calculate the total repayment and monthly payment for the dealer finance option.
Read the worked answer
Amount borrowed = 12000 + 300 = $12,300. Simple interest = P × r × t = 12300 × 0.072 × 4 = 12300 × 0.288 = $3,542.40. Total repayable = 12300 + 3542.40 = $15,842.40. Monthly payment = 15842.40 / 48 = $330.05 (to the cent).
Note the fee is borrowed, so interest is charged on it: the $300 fee actually costs 300 × 1.288 = $386.40 over the term. Monthly payment of about $330 exceeds Sam's $300 comfort level.
2. Estimate the bank loan's monthly repayment and total cost, and compare.
Read the worked answer
Monthly rate i = 0.065/12 ≈ 0.0054167; n = 48. Repayment R = P × i / (1 − (1+i)^−n). (1+i)^48 ≈ e^(48 × ln1.0054167) ≈ e^(48 × 0.005402) ≈ e^0.2593 ≈ 1.2961. (1+i)^−48 ≈ 0.7716, so denominator = 1 − 0.7716 = 0.2284. R = 12000 × 0.0054167 / 0.2284 ≈ 65.00 / 0.2284 ≈ $284.60 per month. Total repayments = 48 × 284.60 ≈ $13,661; plus the $250 upfront fee = ≈ $13,911 total cost.
Comparison: bank ≈ $13,911 vs dealer ≈ $15,842 - the bank is about $1,930 cheaper and its monthly payment ($285) fits Sam's $300 budget, while the dealer option ($330) does not.
3. Which loan is riskier if Sam misses a payment, and does that change the recommendation?
Read the worked answer
The dealer loan is simple interest on a fixed principal: a missed payment does not increase the interest charged (interest is already fixed at $3,542.40), but arrears fees and possible default action apply. The bank loan is reducing-balance: missing a payment means the balance does not reduce as planned, and interest compounds on the higher balance, so the debt grows and the term lengthens.
So the bank loan carries more financial risk from missed payments, even though it is cheaper if paid on schedule. The judgement call: the recommendation should be conditional. If Sam's income is stable, the bank loan is clearly better (cheaper and affordable). If his income is uncertain, the fixed-interest dealer loan's cost is predictable, but at ~$330/month it already exceeds his budget, so neither is safe without a buffer. The defensible answer names the condition rather than declaring one loan universally better.