ARM Calculator Formula

Understand the math behind the arm calculator. Each variable explained with a worked example.

Use the ARM Calculator

Formulas Used

ARM Initial Payment

initial_payment = pmt_init

Estimated Payment After Adjustment

adjusted_payment = pmt_adj

Fixed Rate Payment (comparison)

fixed_payment = pmt_fixed

Monthly Savings During Fixed Period

initial_savings = pmt_fixed - pmt_init

Total Savings During Fixed Period

total_initial_savings = (pmt_fixed - pmt_init) * n_fixed

Balance at Rate Adjustment

remaining_balance = balance_at_adj

Variables

VariableDescriptionDefault
loan_amountLoan Amount(USD)400000
initial_rateInitial ARM Rate(%)5.75
fixed_period_yearsInitial Fixed Period(years)5
adjusted_rateExpected Rate After Adjustment(%)7.75
fixed_rate_comparisonComparable Fixed Rate(%)6.75
loan_term_yearsTotal Loan Term(years)30
r_initDerived value= initial_rate / 100 / 12calculated
r_adjDerived value= adjusted_rate / 100 / 12calculated
r_fixedDerived value= fixed_rate_comparison / 100 / 12calculated
n_totalDerived value= loan_term_years * 12calculated
n_fixedDerived value= fixed_period_years * 12calculated
n_remainingDerived value= n_total - n_fixedcalculated
pmt_initDerived value= r_init > 0 ? loan_amount * r_init * pow(1 + r_init, n_total) / (pow(1 + r_init, n_total) - 1) : loan_amount / n_totalcalculated
balance_at_adjDerived value= r_init > 0 ? loan_amount * (pow(1 + r_init, n_total) - pow(1 + r_init, n_fixed)) / (pow(1 + r_init, n_total) - 1) : loan_amount * (n_total - n_fixed) / n_totalcalculated
pmt_adjDerived value= r_adj > 0 ? balance_at_adj * r_adj * pow(1 + r_adj, n_remaining) / (pow(1 + r_adj, n_remaining) - 1) : balance_at_adj / n_remainingcalculated
pmt_fixedDerived value= r_fixed > 0 ? loan_amount * r_fixed * pow(1 + r_fixed, n_total) / (pow(1 + r_fixed, n_total) - 1) : loan_amount / n_totalcalculated

How It Works

Adjustable-Rate Mortgage (ARM)

An ARM starts with a lower fixed rate for an initial period, then adjusts periodically based on a market index plus a margin.

Common ARM Structures

  • 5/1 ARM: Fixed for 5 years, adjusts annually
  • 7/1 ARM: Fixed for 7 years, adjusts annually
  • 10/1 ARM: Fixed for 10 years, adjusts annually

    • Rate Caps

    ARMs have caps limiting rate changes:

  • Initial cap: Maximum first adjustment (typically 2%)
  • Periodic cap: Maximum annual adjustment (typically 2%)
  • Lifetime cap: Maximum over loan life (typically 5-6%)

    • When an ARM Makes Sense

  • You plan to sell or refinance before the fixed period ends
  • You want to maximize cash flow in the early years
  • You believe rates will stay stable or decrease

    • Worked Example

    A $400,000 loan. 5/1 ARM at 5.75% initial, expected adjustment to 7.75%. Comparable 30-year fixed at 6.75%.

    loan_amount = 400000initial_rate = 5.75fixed_period_years = 5adjusted_rate = 7.75fixed_rate_comparison = 6.75loan_term_years = 30
    1. 01ARM initial payment (5.75%, 30-year amortization): $2,334.29
    2. 02Fixed rate payment (6.75%): $2,594.26
    3. 03Monthly savings during initial period: $2,594.26 - $2,334.29 = $259.97
    4. 04Total savings over 5 years: $259.97 x 60 = $15,598
    5. 05Balance at year 5: approximately $371,342
    6. 06Adjusted payment at 7.75% for remaining 25 years: $2,803.14

    Ready to run the numbers?

    Open ARM Calculator