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Contents

Core Loan Formulas

Monthly Payment Formula

For any amortizing loan (mortgages, auto loans, personal loans), we use the standard payment formula:

M = P × [r(1+r)n] / [(1+r)n - 1]
M = Monthly payment
P = Principal (loan amount)
r = Monthly interest rate (APR ÷ 12)
n = Total number of payments

Total Interest

Total interest paid over the life of a loan:

Total Interest = (M × n) - P

Amortization Schedule

For each payment period, we calculate how much goes to interest vs principal:

Interest = Remaining Balance × Monthly Rate
Principal = Payment − Interest Portion
New Balance = Previous Balance − Principal Portion

Compound Interest

Future Value with Compound Interest

For a lump sum with periodic compounding:

FV = P × (1 + r/n)nt
FV = Future value
P = Principal (initial investment)
r = Annual interest rate (decimal)
n = Compounding frequency per year
t = Time in years

With Monthly Contributions

When adding regular monthly contributions, we use the future value of an annuity:

FV = PMT × [((1 + r)n - 1) / r]

The total future value combines both the initial investment growth and the accumulated contributions.

Simple vs Compound Interest

We show the difference to illustrate the power of compounding:

Simple Interest = P × (1 + r × t)
Compound Benefit = Compound Interest − Simple Interest

HELOC Calculator

Loan-to-Value Ratio (LTV)

LTV measures how much of your home's value is currently mortgaged:

LTV = (Current Mortgage Balance ÷ Home Value) × 100

Example: $200,000 mortgage on a $400,000 home = 50% LTV

Combined Loan-to-Value (CLTV)

CLTV includes your existing mortgage plus the new HELOC:

CLTV = [(Mortgage Balance + HELOC Amount) ÷ Home Value] × 100

Most lenders cap CLTV at 80-85%, meaning you can borrow up to 80-85% of your home's value minus your existing mortgage.

Maximum HELOC Amount

The maximum you can borrow based on your equity and lender limits:

Max HELOC = (Home Value × Max CLTV %) − Current Mortgage Balance

With an 85% max CLTV: $400,000 home × 85% = $340,000 − $200,000 mortgage = $140,000 max HELOC

Interest-Only Payment (Draw Period)

During the draw period, minimum payments cover only interest:

Monthly Interest-Only Payment = (Balance × Annual Rate) ÷ 12

Mortgage Refinance

Monthly Savings

The difference between your current and new monthly payments:

Monthly Savings = Current Payment − New Payment

Break-Even Point

How long until your monthly savings cover the closing costs:

Break-Even (months) = Closing Costs ÷ Monthly Savings

If you plan to stay in your home longer than the break-even period, refinancing likely makes sense. If you might move sooner, the closing costs may not be worth it.

Lifetime Cost Comparison

We compare total costs over the life of each loan:

Current Loan Cost = Remaining Payments × Current Payment
New Loan Cost = (New Term × New Payment) + Closing Costs

Mortgage Affordability

Maximum Home Price Calculation

We use DTI ratios to determine how much you can borrow, then work backwards to find the maximum home price:

Max Monthly Payment = (Gross Income × Max DTI%) − Existing Debts
Max Loan Amount = Calculated using payment formula with max payment
Max Home Price = Max Loan Amount + Down Payment

PITI Components

Monthly housing costs include more than just principal and interest:

P = Principal
I = Interest
T = Property Taxes
I = Insurance (+ PMI if applicable)

Rent vs Buy

Total Cost Comparison

We compare the total financial outcome over your specified time horizon:

Buy Net Position = Home Value − Remaining Mortgage − Total Costs Paid
Rent Net Position = Investment Growth − Total Rent Paid

Opportunity Cost

When renting, we assume your down payment is invested and grows at the specified rate:

Investment Value = Down Payment × (1 + Rate)years

We also account for the monthly savings difference between rent and ownership costs being invested.

Student Loan Payoff

Standard Repayment (10-Year)

Uses the standard loan payment formula with a 120-month term (10 years).

Payment = P × [r(1+r)120] / [(1+r)120 - 1]

Income-Driven Repayment (SAVE Plan Estimate)

The SAVE plan bases payments on discretionary income, which is income above 225% of the federal poverty guideline:

Poverty Guideline = $15,060 + ($5,380 × (Family Size − 1))
Discretionary Income = Annual Income − (Poverty Guideline × 2.25)
Monthly IDR Payment = (Discretionary Income × 5%) ÷ 12

Note: The 5% rate applies to undergraduate loans under SAVE. Graduate loans may use 10%. Actual payments depend on your specific plan and loan servicer.

Credit Card Payoff

Minimum Payment Calculation

Most credit cards calculate minimum payment as:

Minimum Payment = MAX(Floor, Balance × Minimum %)

Typically 1-3% of the balance with a $25-35 floor. Our calculator defaults to 2% with a $25 minimum.

Time to Payoff (Minimum Payments Only)

We simulate month-by-month payments until the balance reaches zero:

Interest This Month = Balance × (APR ÷ 12)
Principal Paid = Payment − Interest
New Balance = Balance − Principal Paid

This iterates each month until balance ≤ 0. With minimum payments, high-interest cards can take decades to pay off.

Minimum Payment Calculator

How Minimum Payments Work

We support three common minimum payment calculation methods:

Percentage of Balance = MAX(Floor, Balance × Min%)
Percentage + Interest = MAX(Floor, Balance × Min% + Interest)
Fixed Amount = Set monthly amount (until balance is lower)

The Minimum Payment Trap

As your balance decreases, so does your minimum payment. This creates a "debt treadmill" where you're always paying just barely more than interest. We simulate month-by-month to show exactly how long payoff takes and compare it to paying a fixed amount.

Balance Transfer

Transfer Cost Analysis

We calculate whether the 0% promo period savings outweigh the transfer fee:

Transfer Fee = Balance × Fee Percentage (typically 3-5%)
Interest Saved = Interest you would have paid on current card
Net Savings = Interest Saved − Transfer Fee

Post-Promo Scenario

If you can't pay off the balance during the 0% period, we calculate remaining interest at the post-promo APR to show the true total cost.

Debt Consolidation

Comparison Methodology

We compare your current debts (paying minimums) versus a single consolidation loan:

Current Path = Sum of all payments until each debt is paid off
Consolidation Path = Total debt × standard amortization at new rate
Weighted Avg Rate = Σ(Balance × Rate) ÷ Total Balance

Auto Loan & Buy vs Lease

Auto Loan Calculator

Uses the standard loan payment formula. We also show total interest and cost breakdown.

Buy vs Lease Comparison

We compare total cost of ownership over your specified time horizon:

Buy Total Cost = Total Payments + Insurance + Maintenance − Resale Value
Lease Total Cost = (Monthly × Term) × Number of Leases + Fees
Mileage Fees = (Miles Over Limit) × Per-Mile Fee

For multi-year comparisons, we assume you would lease multiple vehicles sequentially.

Bi-Weekly Payments

Why Bi-Weekly Saves Money

The math is simple: 26 bi-weekly payments = 13 monthly payments, not 12:

Monthly = 12 payments/year
Bi-Weekly = 26 half-payments = 13 full payments/year
Extra Payment = 1 additional payment per year (goes to principal)

Calculation Method

We simulate both payment schedules and compare: time to payoff, total interest paid, and total amount paid. The bi-weekly schedule applies payments every 2 weeks, reducing average daily balance and saving interest.

Debt-to-Income Ratio

DTI Formula

DTI is the standard measure lenders use to evaluate your borrowing capacity:

DTI = (Total Monthly Debt Payments ÷ Gross Monthly Income) × 100

Under 36%

Healthy

36-43%

Manageable

Over 43%

High Risk

Net Worth Calculator

Net Worth Formula

A simple but powerful calculation:

Net Worth = Total Assets − Total Liabilities

Assets Include:

  • • Cash & bank accounts
  • • Investments (401k, IRA, brokerage)
  • • Property & real estate
  • • Vehicles & other assets

Liabilities Include:

  • • Mortgages
  • • Auto & student loans
  • • Credit card balances
  • • Other debts

Additional Metrics

Liquid Net Worth = Cash + Investments − Non-Mortgage Debt
Debt-to-Asset Ratio = Total Liabilities ÷ Total Assets × 100

Emergency Fund Calculator

Base Calculation

The foundation is your monthly essential expenses:

Recommended Fund = Monthly Expenses × Months Factor

Factor Adjustments

We adjust the recommended months based on your situation:

Factor Impact
Stable employment (government, tenured) −1 to −2 months
Variable income (freelance, commission) +2 to +3 months
Dependents +1 month per dependent
Safety nets (spouse income, family support) −1 to −2 months

Standard recommendation: 3-6 months. Adjusted range: 1-12 months depending on circumstances.

Debt Payoff Strategies

Snowball Method

Focus on quick wins for motivation.

  1. Order debts by balance (smallest first)
  2. Pay minimums on all debts
  3. Put extra money toward smallest balance
  4. When paid off, roll that payment to the next
Best for: People who need psychological wins to stay motivated

Avalanche Method

Minimize total interest paid.

  1. Order debts by interest rate (highest first)
  2. Pay minimums on all debts
  3. Put extra money toward highest-rate debt
  4. When paid off, roll that payment to the next
Best for: Mathematically optimal—saves the most money

Assumptions & Limitations

Assumptions

  • Interest compounds monthly (standard for consumer loans)
  • Payments are made at the end of each month
  • No fees or penalties unless specifically noted
  • Tax implications are not calculated

Limitations

  • Variable rates may change over time
  • Fees, penalties, or other charges not included
  • Tax deductions or credits not considered
  • Promotional rates or special terms not modeled

Disclaimer

These calculators are for educational and informational purposes only. They are not financial advice. Please consult with a qualified financial advisor before making important financial decisions.

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