NPV Comparison Model

Rank every eligible repayment plan by the true cost of borrowing, not just the monthly payment.

Why Net Present Value?

A dollar paid ten years from now costs less than a dollar paid today. Student loan repayment plans differ dramatically in how they spread payments over time: a Standard plan front-loads higher payments over 10 years, while an income-driven plan stretches smaller payments across 20-25 years with a potential forgiveness event. Comparing monthly payments alone ignores the time value of money and any balloon tax liability at the end. NPV captures both.

The Core Formula

NPV = Σ(P_t / (1 + r)^t) + PV(Tax Bomb) − PV(Forgiveness Tax Savings)

Where P_t is the monthly payment at month t, r is the monthly discount rate, and the final two terms account for the lump-sum tax event that occurs when an IDR balance is forgiven after 20 or 25 years.

Plans We Model

Standard (10-year fixed) -- baseline comparison. No forgiveness.
Extended (25-year fixed or graduated) -- lower payments, more interest.
Graduated (10-year escalating) -- payments rise every 2 years.
IBR (Income-Based Repayment) -- 15% of discretionary income, 25-year forgiveness for pre-July 2014 loans; 10% and 20 years for newer loans.
PAYE (Pay As You Earn) -- 10% of discretionary income, 20-year forgiveness.
SAVE / REPAYE -- 5-10% of discretionary income, 20 or 25-year forgiveness depending on loan type.

Discount Rate Selection

The discount rate represents the borrower's opportunity cost of capital -- what they could earn by investing the money instead. Talovex defaults to two benchmarks:

Conservative (3%) -- approximates high-yield savings or Treasury yields, appropriate for risk-averse borrowers.
Market (7%) -- approximates long-term equity returns after inflation, appropriate for borrowers who would invest aggressively.

A higher discount rate makes future payments "cheaper" in today's dollars, which favors plans with longer timelines and potential forgiveness. A lower rate narrows the gap between paying quickly and stretching it out.

Interest Accrual: Daily Simple, Not Compound

Federal student loans accrue interest on a daily simple basis against the outstanding principal -- not compound interest. Many third-party calculators get this wrong. Talovex uses the actual federal formula:

Daily Interest = Outstanding Principal × (Annual Rate / 365.25)

This distinction matters most for IDR plans where payments may not cover accruing interest. Unpaid interest can capitalize (be added to principal) at specific events -- plan changes, loss of partial financial hardship status, or end of deferment -- but it does not compound continuously.

Total Cost of Borrowing

The NPV figure is the single number that captures the all-in cost: every monthly payment, every dollar of capitalized interest, the tax hit on forgiveness, and the time value of money. Plans are ranked from lowest to highest NPV so the cheapest option is always first.

API Reference

POST/v1/compute/npv-comparison

Accepts a borrower profile (loan balance, rate, income, family size, filing status) and returns NPV rankings across all eligible plans at both conservative and market discount rates.

curl -X POST https://talovex-api.smarttechinvest.com/v1/compute/npv-comparison \
  -H "X-API-Key: tlv_your_key" \
  -H "Content-Type: application/json" \
  -d '{
    "balance": 85000,
    "weighted_rate": 0.065,
    "agi": 62000,
    "family_size": 1,
    "filing_status": "single",
    "discount_rates": [0.03, 0.07]
  }'

Response includes plan_rankings[] with NPV at each discount rate, monthly payment schedule summary, total interest paid, and forgiveness amount if applicable.