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Comparing Financial Options
Key Terms
- Always compare options using the same metric: total amount paid, total interest, or effective annual rate
- Flat-rate loan
- interest = principal × rate × time (always charged on original amount)
- Reducing balance loan
- interest charged on outstanding balance — cheaper than flat-rate for the same nominal rate
- Total cost
- = repayment × number of repayments
- Total interest
- = total cost − principal
- Effective annual rate of a flat-rate loan is roughly double the stated rate (interest is paid on the full principal even as it is repaid)
Flat-rate loan interest:
I = PRT (P = principal, R = annual rate, T = years)
Repayment = (P + I) / n
Effective rate comparison:
Total interest / Principal / Years = effective annual rate (approx.)
Reducing balance loan total interest:
Total interest = (P × number of repayments) − Principal
I = PRT (P = principal, R = annual rate, T = years)
Repayment = (P + I) / n
Effective rate comparison:
Total interest / Principal / Years = effective annual rate (approx.)
Reducing balance loan total interest:
Total interest = (P × number of repayments) − Principal
Worked Example: Compare a $10 000 loan over 3 years at: (A) flat rate 6% p.a., (B) reducing balance 6% p.a. monthly.
Option A (flat rate):
Interest = 10 000 × 0.06 × 3 = $1 800
Monthly repayment = (10 000 + 1 800) / 36 = $327.78
Total cost = $11 800
Option B (reducing balance, r = 0.5%/month):
Monthly repayment ≈ $304.22 (using annuity formula)
Total cost = 304.22 × 36 = $10 951.92
Total interest = $951.92
Option B saves $848 in interest despite the same stated rate.
Option A (flat rate):
Interest = 10 000 × 0.06 × 3 = $1 800
Monthly repayment = (10 000 + 1 800) / 36 = $327.78
Total cost = $11 800
Option B (reducing balance, r = 0.5%/month):
Monthly repayment ≈ $304.22 (using annuity formula)
Total cost = 304.22 × 36 = $10 951.92
Total interest = $951.92
Option B saves $848 in interest despite the same stated rate.
Hot Tip: A flat-rate loan charges interest on the original balance even after most has been repaid — you pay interest on money you no longer owe. This is why the effective rate of a flat-rate loan is much higher than the stated rate, even though they look the same at first glance.
Why Compare Financial Options?
Financial products are often marketed with headline figures (e.g. “only 8% interest!”) that don’t tell the full story. To make sound financial decisions, you need to compare products using consistent measures: total interest paid, total amount paid, or effective annual rate.
Flat-Rate vs Reducing Balance Loans
These are the two main loan types you’ll compare:
- Flat-rate: interest is calculated on the original principal for the full term, then added to the principal and divided into equal repayments. Simple to calculate, but expensive — you pay interest on the full amount even after most of it is repaid.
- Reducing balance: interest is charged on the outstanding balance each period. As you repay, the interest bill shrinks. For the same stated rate, this is always cheaper than flat-rate.
Effective Annual Rate
The effective rate of a flat-rate loan is approximately double the stated rate, because on average you owe about half the original principal over the life of the loan, yet pay interest on the full amount.
Comparing Investment Options
The same principles apply to investments: compare total return, total interest earned, or future values over the same time period. A higher stated rate doesn’t always mean higher return if compounding frequency differs.
Strategy: Always calculate total cost and total interest for each option. Don’t just compare monthly repayments — a smaller monthly payment over a longer term can cost far more in total.
Mastery Practice
- Fluency A $5 000 flat-rate loan charges 8% p.a. over 2 years. Find the total interest charged and the monthly repayment.
- Fluency A $5 000 reducing balance loan charges 8% p.a. (monthly rate 0.667%) over 2 years (24 months). The monthly repayment is $226.14. Find the total interest paid.
- Fluency A $12 000 flat-rate loan charges 10% p.a. over 3 years. Calculate: (a) total interest (b) monthly repayment (c) total amount paid.
- Fluency Two savings accounts both offer 5% p.a.: Account A compounds annually, Account B compounds monthly. Which gives a higher balance after 3 years on a $10 000 deposit? Calculate both.
- Understanding A $20 000 car loan is offered as either: (A) flat rate 7% p.a. over 4 years, or (B) reducing balance 7% p.a. (monthly rate 0.583%) with monthly repayments of $478.92 over 4 years (48 months). Compare the total interest paid for each option.
- Understanding A borrower has two loan offers for $15 000 over 5 years: Loan X charges a flat rate of 6% p.a. Loan Y is a reducing balance loan with monthly repayments of $290. Determine which loan has the lower total cost.
- Understanding A $30 000 loan is available over 5 years at a reducing balance rate of 9% p.a. (0.75% monthly). Monthly repayments are $622.75. How much less interest is paid if the borrower makes $800 monthly repayments instead and pays the loan off early? (Iterate to find when Vn = 0 with $800 payments.)
- Understanding Mia has $50 000 to invest for 5 years. Option A: term deposit at 4.2% p.a. compounded annually. Option B: savings account at 4.0% p.a. compounded monthly. Which option gives more money after 5 years?
- Problem Solving A $25 000 personal loan is offered at:
- Option A: flat rate 9% p.a. over 3 years
- Option B: reducing balance 11% p.a. (monthly rate 0.917%) over 3 years (36 months), with repayments of $817.84/month
- Problem Solving Noah is choosing between two home loans for $450 000:
- Loan A: 4.5% p.a. (0.375% monthly), 30-year term, monthly repayments of $2 280.08
- Loan B: 4.8% p.a. (0.4% monthly), 25-year term, monthly repayments of $2 567.24