Analyze lending products including mortgages, HELOCs, and personal loans with amortization and comparison tools. Use when the user asks about mortgage comparison, fixed vs ARM rates, loan qualification, amortization schedules, extra payments, or buying points. Also trigger when users mention 'monthly payment calculation', '15-year vs 30-year mortgage', 'PMI', 'APR vs interest rate', 'HELOC', 'home equity', 'should I buy down the rate', 'biweekly payments', or ask how much house they can afford.
Analyze lending products including mortgages, HELOCs, and personal loans. This skill covers loan comparison, qualification assessment, fixed vs adjustable rate analysis, amortization with extra payments, and home equity line of credit evaluation.
6 — Personal Finance
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The interest rate and monthly payment remain constant for the life of the loan:
Rate is fixed for an initial period, then adjusts periodically based on an index plus a margin:
The standard amortization formula for a fixed-rate loan:
Additional principal payments reduce the outstanding balance, shorten the loan term, and reduce total interest:
Prepaid interest that reduces the loan's interest rate:
A revolving credit line secured by home equity:
Required when conventional loan LTV exceeds 80%:
| Formula | Expression | Use Case |
|---|---|---|
| Monthly payment | PMT = P × [r(1+r)^n] / [(1+r)^n - 1] | Fixed-rate loan payment |
| Total interest | n × PMT - P | Total cost of borrowing |
| Remaining balance after k payments | B_k = P × [(1+r)^n - (1+r)^k] / [(1+r)^n - 1] | Balance at any point |
| Points breakeven | Cost of points / monthly savings | Months to recoup points |
| LTV | Loan amount / property value | Risk and PMI assessment |
| CLTV | (First mortgage + HELOC) / home value | Combined leverage |
| ARM fully indexed rate | Index + margin | Rate after fixed period |
Given: Home price $500K, down payment $100K, loan amount $400K. 30-year rate: 6.5%. 15-year rate: 5.9%. Calculate: Monthly payments, total interest, and interest savings. Solution:
Given: $300K 30-year mortgage at 6.5% (payment = $1,896/mo). Borrower adds $200/month extra to principal. Calculate: Years saved and interest saved. Solution:
See scripts/lending.py for computational helpers.