EMI
Also written Equated Monthly Instalment
The Equated Monthly Instalment — the fixed monthly payment on a loan that covers both interest and a portion of the principal, calculated so the loan is fully repaid by the end of its term.
In plain language
Most loans in India are repaid the same way: a fixed amount every month, for a set number of months, until the loan is cleared. That fixed monthly payment is the EMI — the Equated Monthly Instalment.
Every EMI is really two payments combined into one. Part of it pays the interest for that month; the rest reduces the amount still owed, the principal. Early in a loan, most of the EMI goes towards interest. As the loan gets repaid, more of each EMI goes towards principal instead.
Knowing the EMI in advance lets a borrower check, before signing for a loan, whether the monthly outflow is actually affordable.
How it works
An EMI is calculated using Excel's PMT function, with three inputs: r, the interest rate for the loan; Nper, the number of periods over which it is repaid; and PV, the loan amount itself. Because most home loans reset monthly, the annual rate is divided by 12, and the number of years is multiplied by 12 to get the number of monthly periods.
Satish wants a Rs 30,00,000 home loan over 20 years at 6.5%, resetting monthly. That means r = 0.065/12 and n = 240 months:
PMT(0.065/12, 240, -30,00,000) = Rs 22,367
If the rate later falls to 6.25%, the same loan's EMI drops to Rs 21,928 — a fall of Rs 439 a month for a quarter-point rate cut, on this same 20-year, Rs 30 lakh loan.
A worked example
Satish takes the Rs 30,00,000, 20-year home loan above at 6.5%, with an EMI of Rs 22,367. Over the loan's life he will pay 22,367 × 240 = Rs 53,68,080 in total — of which Rs 23,68,080 is interest, on top of the Rs 30,00,000 principal.
Had he instead chosen a 15-year term at the same 6.5%, PMT(0.065/12, 180, -30,00,000) works out to a higher EMI of roughly Rs 26,140, but with far less total interest paid over the shorter term. The EMI figure alone does not tell the whole story — the total interest paid over the life of the loan is the other half of the decision.
Why NISM asks about it
Chapter 2 (Time Value of Money), section 2.2.4 (Periodic investments or pay-outs), works through the Satish home-loan example in full, including the sensitivity to a rate change. Expect a PMT-style calculation given a loan amount, rate and tenor, and a conceptual question on why the same rate change produces different EMI changes for different loan sizes or tenors.
Common exam traps
- Divide the annual rate by 12 and multiply the years by 12 for a monthly-reset loan — both adjustments are needed together, and forgetting either gives a wrong EMI.
- A lower EMI from a longer tenor is not automatically cheaper overall — see debt rescheduling for the present-value check that catches this.
- The EMI is not just interest — it always contains a principal component too, even in the first month of the loan.
Check yourself
1.A Rs 5 lakh loan at 8 per cent is repaid with an EMI of Rs 12,000. NPER returns 48.97. What does this represent?
- a)48.97 years
- b)48.97 months
- c)48.97 quarters
- d)48.97 instalments of interest only
Show the answer
Answer: (b) 48.97 months
Because the rate was entered as 0.08/12, the function works in monthly periods, so "the result is 48.97 MONTHS. This gives a clear idea about the time period in which the payment would be complete." The chapter notes NPER is useful to calculate the repayment period and match it with an affordable EMI.
2.Rs 100 invested grows to Rs 120 in 2 years. Which Excel entry does the chapter use to find the CAGR, and what result does it give?
- a)=RATE(2,,-100,120), giving 0.0954 or 9.54 per cent
- b)=PMT(2,-100,120), giving 9.54 per cent
- c)=FV(2,,-100,120), giving 120
- d)=RATE(120,,-100,2), giving 0.10 or 10 per cent
Show the answer
Answer: (a) =RATE(2,,-100,120), giving 0.0954 or 9.54 per cent
The chapter: "In Excel the CAGR can be found out by the Rate Formula — CAGR = RATE(Years,,-PV,FV)". For this example, NPER (years) = 2, PV = -100, FV = 120, so "=RATE(2,,-100,120) = 0.0954 or 9.54%".
By the formula method the same answer is ((120/100)^(1/2)) − 1 = 1.0954 − 1, which the chapter rounds to 9.5%.
Option B is wrong because PMT gives the periodic payment, such as an EMI, from the rate, number of periods and present value. It does not solve for a rate.
Option C is wrong because FV gives a future value from a known rate. Here the future value (Rs 120) is already known and the rate is the unknown.
Option D is wrong because the arguments are in the wrong order. The syntax puts the number of years first, then the present value (negative) and then the future value. Getting 10 per cent is also the trap of dividing the 20 per cent gain by 2 years, which ignores compounding.
3.A borrower earning Rs 10,000 a month has an EMI of Rs 2,224.44. To bring the burden down, he extends the tenor from 5 to 6 years, so the EMI becomes Rs 1,955.02. He also has another loan with a repayment of Rs 1,000 a month. What is his debt servicing ratio now?
- a)22.24 per cent
- b)19.55 per cent
- c)32.24 per cent
- d)29.55 per cent
Show the answer
Answer: (d) 29.55 per cent
This follows the chapter's worked example in section 4.9.
Total debt servicing = Rs 1,955.02 + Rs 1,000 = Rs 2,955.02. Debt servicing ratio = 2,955.02 ÷ 10,000 = 29.55%.
The chapter: "If the borrower has another loan on which repayment is Rs1,000 per month, then total debt servicing is Rs1,955.02+ Rs1,000 i.e. Rs2,955.02. Debt servicing ratio would then be 29.55%." Debt servicing counts all payments due to lenders.
Option A (22.24%) is wrong because it is the ratio on the original 5-year EMI alone, before the extension and without the second loan.
Option B (19.55%) is wrong because it is the revised ratio on the extended loan alone. It leaves out the second loan's Rs 1,000.
Option C (32.24%) is wrong because it adds the Rs 1,000 to the old EMI of Rs 2,224.44 instead of the revised Rs 1,955.02.
Context: the chapter names three ways to reduce the ratio — "increasing the tenor or reducing the interest cost or reducing the amount borrowed". A longer tenor lowers the EMI, but the chapter also notes that a longer tenor loan "translates into higher interest paid over the term".
Where this is taught
Free preparation for NISM Series X-ARelated terms
- Debt reschedulingA change to the terms of an existing loan — a lower EMI, a longer tenor, or a lower rate — agreed with the lender when a borrower can no longer service it as originally structured.
- Debt servicingAll payments a borrower owes a lender, whether principal or interest — the actual monthly outflow that every EMI, card payment and instalment adds up to, before it is turned into any ratio.
- Discount rateThe rate used to bring a future cash flow back to today's value — the higher this rate, the lower a given future amount is worth in present-day rupees.
- Fixed annuityAn annuity that pays a fixed, unchanging amount at each regular period, agreed at the time of investing — as against a floating annuity, whose payouts move with an inflation or index benchmark.
- LeaseA contract in which the owner of an asset, the lessor, lets another person, the lessee, use it for a period in exchange for lease payments — and keeps ownership throughout.
- MortgageA loan secured by a charge on the property it funds: the borrower keeps the asset in his own name, and the lender can take it over and sell it if the loan is not repaid.
- NPER functionThe Excel function that returns how many periods a loan takes to clear, given the rate, the instalment and the amount outstanding — the workbook's tool for the period of the loan.
- PPMT and IPMTThe two spreadsheet functions that split a single loan instalment into its principal part (PPMT) and its interest part (IPMT), for any instalment number you name.
- Staggering of goalsPushing a financial goal further out in time, instead of cancelling it, when the household's current finances cannot fund it in the period originally wanted.
- Credit scoreThe number a credit information company builds from your loan and credit-card repayment history, and the first thing a lender looks at when your application arrives.
- Emergency fundA pool of money held in liquid assets, sized at six months of household expenses, kept aside so that an interruption in income does not force the sale of long-term investments.
- AmortisationThe repayment of borrowed capital over a fixed term through equal instalments, each of which is split between interest and principal in proportions that shift over the life of the loan.
- Pre-EMI interestInterest-only monthly payments on a loan that has not yet been fully disbursed — typical of home loans for under-construction property — before full EMIs of principal and interest begin.
- RestA lender's interest-charging cycle — how often the outstanding loan is recomputed for interest — which can differ from the repayment cycle and raise the true cost of a loan.
- PrepaymentRepaying part or all of a loan's capital before it is due, which reduces the outstanding principal and the remaining EMI period — subject to any lock-in or prepayment charges.
- Floating rate loanA loan whose interest rate is reset periodically in line with the benchmark it is linked to — such as the repo rate or a bank's MCLR — so the EMI or tenure changes as rates move.
- Fixed rate loanA loan whose interest rate stays the same for the entire tenure, fixed at the time of borrowing — useful for locking in a low rate, as against a floating rate loan whose rate resets with a benchmark.
- Home equity loanA loan against property, or LAP, where the borrower pledges their own home as collateral to raise funds for any purpose, capped by the property's value and the lender's advance rate.