Northspread
Formula sheet/NISM Series X-A: Investment Adviser (Level 1)/Personal Financial Planning
[ PERSONAL FINANCIAL PLANNING ]

Loan Amortization, EMI, PPMT, IPMT & NPER

Equated Monthly Instalment(EMI):EMI=[P×r×(1+r)n]/[(1+r)n−1]\text{Equated Monthly Instalment} (EMI): EMI = [ P \times r \times (1 + r)^{n} ] / [ (1 + r)^{n} - 1 ]
Excel: =PMT(r, n, -P)
Principal Component in Period t: =PPMT(r, t, n, -P) | Interest Component in Period t: =IPMT(r, t, n, -P)
Loan Tenor(NPER):=NPER(r,−PMT,P)=ln(1−[P×r/PMT])/ln(1+r)\text{Loan Tenor} (NPER): =NPER(r, -PMT, P) = ln( 1 - [ P \times r / PMT ] ) / ln( 1 + r )
Variables

P: Loan principal; r: Monthly rate (Annual Rate / 12); n: Total months (Years × 12); t: Period index.

Exam note

In early loan periods, interest forms the bulk of the EMI; as the principal balance reduces, the principal repayment component accelerates.

Worked examples
Home Loan EMI & Monthly Amortization Breakdown (PPMT & IPMT)

A borrower avails a Home Loan of Rs 30,00,000 at 6.50% p.a. interest for a tenor of 20 years (240 months). Calculate the monthly EMI. Additionally, calculate the exact Principal (PPMT) and Interest (IPMT) components for the 1st monthly instalment and the 61st monthly instalment.

Loan Restructuring & Tenure Extension PV Comparison

A borrower has an outstanding loan balance of Rs 20,00,000 with 10 years remaining at 10.0% p.a. (Existing EMI = Rs 26,430). Facing cash flow constraints, the bank offers to extend the tenure to 15 years at 10.5% p.a. (New EMI = Rs 22,108). If the borrower's opportunity cost of capital is 8.0% p.a., calculate the PV of both repayment streams and determine the financial cost of restructuring.

Personal Financial Health & Leverage Diagnostic Ratios

A client presents the following financial profile: Annual Gross Salary = Rs 15,00,000; Annual Savings (PF, MF, Deposits) = Rs 4,50,000; Monthly Debt Servicing = Rs 45,000. Balance Sheet: Self-occupied house = Rs 75,00,000, Home Loan outstanding = Rs 45,00,000, Liquid Assets (Savings Bank + Liquid MFs) = Rs 9,00,000, Total Financial Assets = Rs 25,00,000, Total Debt Liabilities = Rs 50,00,000. Monthly living expenses = Rs 45,833. Compute Savings Ratio, Leverage Ratio, Solvency Ratio, Liquidity Ratio, and Debt-to-Income (DTI) Ratio.