Common mistake 1 with EMI / home loan planner

Comparing loans on the EMI alone. A lower EMI over a longer term can cost much more in total interest.

Common mistake 2 with EMI / home loan planner

Assuming a floating-rate loan's schedule is fixed - it holds only until the next rate reset.

Common mistake 3 with EMI / home loan planner

Treating the tax deduction as unlimited. In India the Section 24 interest deduction on a self-occupied house is capped at ₹2,00,000 a year, so the after-tax saving shown here is an upper bound.

Common mistake 4 with EMI / home loan planner

Prepaying every spare rupee and leaving no emergency buffer - the prepayment is illiquid, an investment is not.

Common mistake 5 with EMI / home loan planner

Forgetting prepayment penalties (rare on floating-rate home loans, common elsewhere), processing fees and loan insurance.

Common mistake 6 with EMI / home loan planner

Comparing loans on the instalment rather than the total cost. A longer term always gives a smaller instalment and almost always costs more.

EconStatsCraft › EMI / home loan planner

EMI / home loan planner

Models a real home loan: the instalment and full amortisation, then any mix of prepayments - a monthly top-up, a yearly bonus, a one-time lump - with the choice to shorten the tenure or cut the EMI, an after-tax view of the interest saved, and a side-by-side of prepaying versus investing the same surplus.

The intuition

An equated monthly instalment is the constant payment that exactly retires a loan over its term. Every payment splits into interest on what you still owe and repayment of principal, and because the balance falls, the split shifts steadily from interest towards principal. Early payments are almost entirely interest, which is why paying off a loan early saves so much and why the total interest on a long loan can exceed the amount borrowed.

When to use it

Any amortising fixed-rate loan - a mortgage, a car loan, a personal loan - where you want the payment, the total interest cost, the amortisation schedule, or the effect of paying a bit extra each month.

Where the estimator comes from

The balance after N payments must be zero. With monthly rate i=r/12, the present value of N payments of A is an annuity, A\frac{1-(1+i)^{-N}}{i}, and setting that equal to the principal P gives A=\frac{P\,i\,(1+i)^N}{(1+i)^N-1}. The outstanding balance after k payments is B_k=P(1+i)^k-A\frac{(1+i)^k-1}{i}, which is the compounded original debt less the compounded value of what has been paid. Interest in month k is i\,B_{k-1}, and everything else in the payment reduces principal.

The model

\text{EMI} = P\,\frac{r(1+r)^{n}}{(1+r)^{n}-1},\qquad r = \frac{\text{annual rate}}{12},\quad n = \text{months}

What it assumes

The interest rate is fixed for the whole term. A floating-rate loan recalculates the EMI or the tenure at each reset.
Interest compounds monthly and the first payment falls one month after the loan is drawn.
No processing fee, insurance or other charge is folded into the payment.
The payment frequency matches the compounding frequency. A monthly instalment on an annually compounded loan is not what this formula computes, and the difference over a long term is substantial.

Statistical properties

The rate must be converted to the payment frequency. An annual 8.5% becomes a monthly 0.7083%, not 8.5%, and this single conversion is the most common error in the whole calculation.
Total interest grows faster than linearly in the term. Doubling a loan from 10 to 20 years roughly triples the interest paid, because the balance stays high for much longer.
The interest share of the payment declines geometrically, not linearly. Principal only overtakes interest well past the halfway point of a long loan.
A prepayment reduces the balance directly, so the interest it saves is the rate compounded over the whole remaining term. Prepaying early is worth far more than prepaying late.
The flat-rate quote used by some lenders charges interest on the ORIGINAL principal for the whole term. That is roughly double the true effective rate, and comparing it against a reducing-balance rate is the standard mis-selling.
This assumes a fixed rate. On a floating loan the lender normally holds the instalment constant and changes the term instead, which hides the impact of a rate rise.

How to read the output

Total interest as a percentage of the amount borrowed shows the real cost of a long tenure - a 20-year loan often repays more in interest than the sum borrowed.
In the first EMI almost the whole payment is interest; in the last one almost none is. The crossover is roughly two-thirds of the way through a typical mortgage.
A prepayment can either shorten the tenure (keep the EMI) or cut the EMI (keep the tenure). Shortening the tenure saves far more interest; cutting the EMI eases monthly cash flow. This planner does both.
Money prepaid EARLY works hardest - a lump sum in year 3 removes principal that would otherwise accrue interest for 17 more years.
Prepay-or-invest: prepaying is a guaranteed return equal to the loan's after-tax rate. Invest the surplus instead only if you can reliably beat that, after tax and after allowing for risk.
The early payments are mostly interest and the late ones mostly principal, even though the instalment is constant. The outstanding balance therefore falls slowly at first, which is why prepaying early saves far more than prepaying late.
Total interest paid is roughly proportional to the term for a given rate, so extending a loan to reduce the instalment is rarely the cheap option it appears to be.
The rate quoted and the rate used must be on the same basis. A nominal annual rate divided by twelve is not the same as an effective monthly rate, and the difference compounds over the term.

A worked reading

Five million over twenty years at 8.5% gives an EMI of 43,391. Over 240 payments that is 10,413,879 in total, of which 5,413,879 is interest - 108% of the amount borrowed. The first payment is 35,417 of interest and only 7,974 of principal, so 82% of the first cheque never touches the debt. Principal does not exceed interest within a single payment until month 143, almost twelve years in. That asymmetry, rather than the headline rate, is what makes early prepayment so effective.

Symptom → diagnosis → what to do

If you see this	It means	Do this
EMI implausibly large	Annual rate not divided by 12	The commonest error
Balance not reaching zero at the end	Rounding accumulated over the schedule	The final payment is normally adjusted for this
Total interest exceeding the principal	Correct for a long loan at a moderate rate	Not an error. It surprises people, which is the point of showing it
Two lenders quoting the same rate with different EMIs	One is a flat rate, the other reducing balance	Compare the effective annual rate, never the headline
Doubling the term does not halve the EMI	Correct. The relationship is not linear	It approaches an asymptote set by the interest alone
A small rate change moving the EMI a lot	Long term, so heavy discounting	Sensitivity rises with the term

Common mistakes

Comparing loans on the EMI alone. A lower EMI over a longer term can cost much more in total interest.
Assuming a floating-rate loan's schedule is fixed - it holds only until the next rate reset.
Treating the tax deduction as unlimited. In India the Section 24 interest deduction on a self-occupied house is capped at ₹2,00,000 a year, so the after-tax saving shown here is an upper bound.
Prepaying every spare rupee and leaving no emergency buffer - the prepayment is illiquid, an investment is not.
Forgetting prepayment penalties (rare on floating-rate home loans, common elsewhere), processing fees and loan insurance.
Comparing loans on the instalment rather than the total cost. A longer term always gives a smaller instalment and almost always costs more.
Assuming a quoted flat rate is comparable with a reducing-balance rate. A flat rate charges interest on the original principal throughout, so the effective reducing-balance rate is close to double it.
Ignoring fees folded into the disbursed amount. The instalment is computed on the loan, but the money received is the loan minus the fee, and the effective rate is higher than the quoted one.
Treating an amortisation schedule as fixed. Any prepayment changes every row after it, and lenders differ in whether they shorten the term or reduce the instalment.

Where to read this properly

Brealey, Myers and Allen, Principles of Corporate Finance (2020), ch. 2, on annuities.
Reserve Bank of India (2016, updated periodically), Master Direction - Reserve Bank of India (Interest Rate on Advances) Directions, 2016, DBR.Dir.No.85/13.03.00/2015-16, issued 3 March 2016 - on how interest on advances is to be charged.
Bodie, Kane and Marcus, Investments (2021), ch. 14, on the term structure behind the discounting.

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EMI / home loan planner

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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