Hong Life CalculatorsUnderstanding the loan comparison calculator — concept and principle
This calculator puts two fixed-rate loans side by side for the same amount. It shows each monthly payment, total interest, the full cost including upfront fees, and an APR that includes those fees, so you can see which offer is really cheaper.
How it is calculated
- Monthly payment = P × r ÷ (1 − (1 + r)^−n), with r = annual rate ÷ 12 and n = months.
- Total interest = payment × n − P.
- Cost of the loan = total interest + upfront fees.
- APR with fees: the monthly rate at which the payments exactly repay only the money you actually receive (P − fees), times 12. It is found by bisection.
- Saving = the difference in total cost between the two loans.
The principle
A lower interest rate does not always mean a cheaper loan. Fees paid at the start reduce the money you actually get while the payments stay the same, so the effective rate rises. Converting each loan into an APR that includes fees puts both offers on one scale, which is the idea behind US Truth in Lending disclosures. Comparing the total cost in money is the most direct check when the terms are the same length.
Worked example
Default inputs: 25,000 USD; loan A 7.5% for 5 years, no fees; loan B 6.9% for 5 years, 750 USD fees.
- Loan A payment = 25,000 × 0.00625 ÷ (1 − 1.00625^−60) ≈ 500.95 USD; interest ≈ 5,056.92 USD.
- Loan B payment ≈ 493.85 USD; interest ≈ 4,631.08 USD; plus fees = 5,381.08 USD.
- Loan A total cost 5,056.92 USD vs loan B 5,381.08 USD: Loan A costs less.
- Saving = 5,381.08 − 5,056.92 = 324.16 USD.
- APR with fees: loan A 7.5%, loan B 8.18%, because B's payments repay only 24,250 USD received.
| Loan B: interest rate (% a year) | Saving with the cheaper loan |
|---|---|
| 1.73 | $3,195.35 |
| 3.45 | $2,052.88 |
| 5.17 | $879.65 |
| 6.9 | $324.16 |
| 8.62 | $1,558.32 |
| 10.3 | $2,822.58 |
| 13.8 | $5,440.12 |
How to read the result
Choose the loan with the lower total cost if you will keep it to the end. If you might repay early, fees weigh even more, because they are paid in full while interest stops. When terms differ, a longer term usually lowers the payment but raises total interest; decide whether you value monthly cash flow or total cost.
Common mistakes
- Comparing headline rates while ignoring origination fees.
- Comparing a 3-year loan with a 5-year loan only by monthly payment.
- Forgetting prepayment penalties or rate changes on variable loans.
- Including optional insurance in one offer but not the other.
Frequently asked questions
Is the lower interest rate always better?
No. In the default example the 6.9% loan costs more because of its 750 USD fee.
What does APR with fees mean?
It is the rate that links what you actually receive with what you pay back, so fees show up in the rate.
How do I compare loans with different terms?
Look at total cost and at the monthly payment, and decide which matters more to you.
Sources: Consumer Financial Protection Bureau, Regulation Z, 12 CFR Part 1026, Appendix J · CFPB, "What is the difference between a loan interest rate and the APR?"