How can I calculate the total interest paid over the life of my loan?

As a homeowner with a fixed-rate mortgage that started five years ago with an original balance of $250,000 at a 4.25% APR over 30 years, I’ve been making consistent monthly payments. Recently, I’ve been considering refinancing to a shorter 20-year term at 3.75% and want to compare the lifetime costs. My current loan includes PMI that just dropped off this year, but there was an upfront origination fee at closing. To make a truly informed financial decision, how can I calculate the total interest paid over the life of this new hypothetical loan while accounting for its specific terms, fees, and accelerated repayment schedule? Are there standard formulas, spreadsheet methods, or free online calculators that can break this down for me?

To calculate the total interest paid over the life of a loan, follow these steps based on the type of loan structure (amortized loans are most common, e.g., mortgages, auto loans):

For Amortized Loans (Fixed Monthly Payments)

1. Gather Loan Details:

   • Principal (P): The initial loan amount.
   • Annual Interest Rate (r): Expressed as a decimal (e.g., 5% = 0.05).
   • Loan Term (t): The total time in years.
   • Payments per Year (m): Typically 12 for monthly payments.

2. Calculate the Monthly Payment (M):
   Use the amortization formula:
   [
   M = P \times \frac{r/m \times (1 + r/m)^{n}}{(1 + r/m)^{n} – 1}
   ]

   • n: Total number of payments ((n = t \times m)).
   • Example: For a $200,000 loan at 5% annual interest over 30 years (360 monthly payments):
     • (r/m = 0.05/12 = 0.0041667)
     • (n = 30 \times 12 = 360)
     • (M = 200,!000 \times \frac{0.0041667 \times (1.0041667)^{360}}{(1.0041667)^{360} – 1} \approx \$1,!073.64)

3. Compute Total Payments:
   [
   \text{Total Payments} = M \times n
   ]

   • Example: (1,!073.64 \times 360 = \$386,!510.40)

4. Calculate Total Interest:
   [
   \text{Total Interest} = \text{Total Payments} – P
   ]

   • Example: (386,!510.40 – 200,!000 = \$186,!510.40)

For Simple Interest Loans (Non-Amortized)

1. Gather Loan Details:

   • Principal (P).
   • Annual Interest Rate (r).
   • Loan Term (t) in years.

2. Calculate Total Interest:
   [
   \text{Total Interest} = P \times r \times t
   ]

   • Example: A $10,000 loan at 6% interest for 3 years:
     • Total Interest = (10,!000 \times 0.06 \times 3 = \$1,!800)

Key Notes

• Amortization: Each payment includes both principal and interest; interest decreases over time.
• Simple Interest: Interest is calculated only on the original principal, not reducing balance.
• Tools: Use online calculators (e.g., Bankrate, NerdWallet) or spreadsheets (Excel’s PMT function for amortized loans) for accuracy.
• Variables: Adjustable-rate loans (ARMs) require recalculating periodically as rates change.

Example Summary

Always refer to your loan agreement for precise terms, as fees or prepayments may affect the total.