Loan Comparison Calculator

What the Loan Comparison Calculator Does (and What It Assumes)

A loan comparison is really two calculations run side by side: the monthly payment for each loan and the total interest paid over the full term. ProcalcAI’s Loan Comparison Calculator takes one Loan Amount and compares:

- Loan A Rate (%) and Loan A Term (years) - Loan B Rate (%) and Loan B Term (years)

It then shows: - Payment A vs Payment B (monthly) - Total Interest A vs Total Interest B (over the entire term) - The interest difference (how much one loan saves vs the other) - A “winner” based on which loan has lower total interest

Important assumption: this is a standard fully amortizing loan with a fixed interest rate and equal monthly payments (like a typical mortgage or installment loan). It does not include fees, points, insurance, taxes, or prepayments unless you account for them separately.

Inputs You Need (and How to Interpret Them)

1. Loan Amount (P) The principal you borrow. Example: 200,000.

2. Interest Rate (%) for each loan Enter the annual nominal rate (APR-style input). The calculator converts it to a monthly rate.

3. Term (years) for each loan The length of the loan in years. The calculator converts it to number of monthly payments.

Key terms to know: - Principal: the amount borrowed (P). - Interest rate: annual rate you enter; converted to monthly. - Monthly rate: r = annual_rate / 12. - Term: years converted to months (n). - Amortization: paying off the loan with fixed monthly payments. - Total interest: total paid minus principal.

The Math Behind the Comparison (Formulas Used)

### Step 1: Convert annual rate to monthly rate For each loan: - r = (rate% / 100) / 12

Example: 6.5% becomes r = (6.5 / 100) / 12 = 0.0054166667 per month

### Step 2: Convert term in years to number of payments - n = term_years × 12

Example: 30 years becomes n = 30 × 12 = 360 payments

### Step 3: Calculate the monthly payment (amortizing loan formula) If r > 0: - Payment = P × [ r(1 + r)^n ] / [ (1 + r)^n − 1 ]

If r = 0 (a true zero-interest loan), the calculator uses: - Payment = P / n

### Step 4: Calculate total interest paid - Total Interest = (Payment × n) − P

### Step 5: Compare loans - Interest Difference = |Interest_A − Interest_B| - Winner = the loan with the smaller total interest

This approach aligns with the standard amortization payment formula commonly used in consumer finance (see Investopedia’s amortization explanation and payment formula discussion: https://www.investopedia.com/terms/a/amortization.asp).

Worked Example 1: 30-Year vs 15-Year (Different Rates)

Loan Amount (P): 200,000 Loan A: 6.5% for 30 years Loan B: 5.75% for 15 years

### Loan A - rA = (6.5/100)/12 = 0.0054166667 - nA = 30×12 = 360 - Payment A ≈ 1,264.14/month - Total Interest A = 1,264.14×360 − 200,000 ≈ 255,090.40

### Loan B - rB = (5.75/100)/12 = 0.0047916667 - nB = 15×12 = 180 - Payment B ≈ 1,660.45/month - Total Interest B = 1,660.45×180 − 200,000 ≈ 98,881.00

### Comparison - Interest Difference ≈ 255,090.40 − 98,881.00 = 156,209.40 - Winner (lower total interest): Loan B - Tradeoff: Loan B costs about 396.31 more per month, but saves about 156,209.40 in interest over the full term.

Worked Example 2: Same Term, Different Rates (Pure Rate Shopping)

Loan Amount: 300,000 Loan A: 7.0% for 30 years Loan B: 6.25% for 30 years

### Loan A - rA = (7/100)/12 = 0.0058333333 - nA = 360 - Payment A ≈ 1,995.91/month - Total Interest A ≈ 1,995.91×360 − 300,000 = 418,527.60

### Loan B - rB = (6.25/100)/12 = 0.0052083333 - nB = 360 - Payment B ≈ 1,846.24/month - Total Interest B ≈ 1,846.24×360 − 300,000 = 364,646.40

### Comparison - Monthly savings with Loan B ≈ 149.67/month - Interest Difference ≈ 53,881.20 - Winner: Loan B

This is the classic use case: when terms match, the lower rate almost always wins on both monthly payment and total interest (assuming no hidden fees).

Worked Example 3: Shorter Term at Higher Rate (Not Always Obvious)

Loan Amount: 150,000 Loan A: 6.8% for 10 years Loan B: 6.2% for 15 years

### Loan A - rA = (6.8/100)/12 = 0.0056666667 - nA = 120 - Payment A ≈ 1,725.04/month - Total Interest A ≈ 1,725.04×120 − 150,000 = 57,004.80

### Loan B - rB = (6.2/100)/12 = 0.0051666667 - nB = 180 - Payment B ≈ 1,281.18/month - Total Interest B ≈ 1,281.18×180 − 150,000 = 80,612.40

### Comparison - Loan A has a higher monthly payment, but lower total interest - Interest Difference ≈ 23,607.60 - Winner: Loan A

Even with a higher rate, the much shorter term can reduce total interest dramatically.

Pro Tips for Making the Comparison More Realistic

1. Compare total cost, not just the monthly payment. A lower payment can hide a much higher total interest bill if the term is longer.

2. Run a “same term” scenario and a “preferred payment” scenario. - Same term isolates the effect of the interest rate. - Different terms show the tradeoff between affordability and interest savings.

3. Account for fees separately. If one loan has origination fees or points, add them to the loan amount (rough approximation) or track them as an extra upfront cost and compare against interest savings.

4. Stress-test your budget. If Loan B saves interest but the payment is tight, the “best” loan on paper may not be the best in real life.

5. Use the winner as a starting point, not the final decision. The calculator’s “winner” is strictly based on total interest over the full term.

Common Mistakes (and How to Avoid Them)

- Mixing up APR and monthly rate. Enter the annual percentage rate; the calculator handles dividing by 12. Don’t pre-divide it yourself. - Comparing loans with different terms without noticing the payment jump. A 15-year option often “wins” on interest but may be unaffordable. - Ignoring the zero-interest edge case. If a promotional loan is truly 0%, the payment is simply principal divided by months. - Assuming you will keep the loan for the full term. This calculator compares full-term interest. If you plan to refinance or sell early, the “winner” could change. - Rounding too early when doing manual math. Keep several decimals for r and only round the final payment and totals.

If you want to replicate ProcalcAI’s results by hand, follow the exact sequence: convert to monthly rate, convert years to months, compute payment with the amortization formula, compute total interest, then compare interest totals.

Authoritative Sources

This calculator uses formulas and reference data drawn from the following sources:

- Bureau of Labor Statistics - HUD — Housing and Urban Development - Federal Reserve — Economic Data

This loan comparison calculator uses standard finance formulas to compute results. Enter your values and the formula is applied automatically — all math is handled for you. The calculation follows industry-standard methodology.

• https://www.irs.gov
• https://www.investor.gov
• https://www.nerdwallet.com