UNIT 10 • INTEREST & FINANCE

EMI Calculator
with Amortisation Schedule

An EMI (equated monthly instalment) is the fixed monthly payment that clears a loan with interest: $EMI = \frac{P\,i\,(1+i)^N}{(1+i)^N - 1}$ . Each EMI pays that month's interest first; the rest reduces the loan.

HOW AN EMI IS WORKED OUTREDUCING BALANCE

\begin{gathered} EMI = \frac{P \, i \, (1 + i)^N}{(1 + i)^N - 1} \\ i = \frac{R}{12 \times 100}, \quad N = \text{months} \end{gathered}

1. Monthly RateDivide the yearly rate by 12 and by 100: 9% a year gives

i = 0.0075

2. MonthsTurn the tenure into months: 5 years is

N = 60

3. Each MonthInterest = balance × i. The rest of the EMI reduces the balance.

Step-by-Step Worked Example

HAND-HOLDING TUTORIAL

OUR PROBLEM TO SOLVE

A car loan of ₹5,00,000 is taken at 9% a year for 5 years. Find the EMI, the total interest, and how the first two EMIs are split.

STEP 01 • MONTHLY RATE AND MONTHS

i = \frac{9}{12 \times 100} = 0.0075, \qquad N = 5 \times 12 = 60, \qquad (1.0075)^{60} = 1.565681

STEP 02 • EMI

EMI = \frac{5{,}00{,}000 \times 0.0075 \times 1.565681}{1.565681 - 1} = \frac{5871.30}{0.565681} \approx 10{,}379.18

STEP 03 • TOTAL INTEREST

\text{Total paid} = 10{,}379.18 \times 60 = 6{,}22{,}750.66

\text{Total interest} = 6{,}22{,}750.66 - 5{,}00{,}000 = 1{,}22{,}750.66

STEP 04 • THE FIRST TWO EMIs

\text{Month 1: interest} = 5{,}00{,}000 \times 0.0075 = 3750, \quad \text{principal} = 10{,}379.18 - 3750 = 6629.18

\text{Month 2: interest} = 4{,}93{,}370.82 \times 0.0075 = 3700.28, \quad \text{principal} = 6678.90

The interest part shrinks each month and the principal part grows, while the EMI stays the same.

FINAL CONCLUSION

EMI ≈ ₹10,379.18 for 60 months

EMI \approx 10{,}379.18, \qquad \text{interest} \approx 1{,}22{,}750.66

The calculator below opens on this loan. Add a prepayment of ₹1,00,000 after month 24 to see it finish a year early.

LABORATORY

Interactive EMI Calculator

LABORATORY

EMI Engine

Loan amount PInterest rate R (% a year)TenureTenure is inCurrency

Interest is charged on

Prepayment (optional)

Extra amount paid onceAfter which month?

Common Questions

What is the EMI formula?

EMI = \frac{P\,i\,(1+i)^N}{(1+i)^N - 1}

, where P is the loan,

i

is the monthly rate (yearly rate ÷ 12 ÷ 100) and N is the number of months.

Why is most of the early EMI interest?

Interest is charged on what you still owe. At the start you owe the most, so the interest part is biggest and only a small part of the EMI reduces the loan. Each month the balance falls, so more of the same EMI goes to principal.

Is a flat rate cheaper than a reducing rate?

Usually not. A flat rate charges interest on the full loan for the whole term, even after you have paid most of it back. A 10% flat rate over one year costs about the same as an 18% reducing rate, and the calculator shows the equivalent for your loan.

Does prepaying a loan save money?

Yes. A prepayment goes straight to the principal, so every later month charges less interest. If you keep the same EMI, the loan ends sooner. Check whether your lender charges a prepayment fee first.

PreviousSimple & Compound Interest

Unit 10•47 of 47

∑

f(x)∫dxπ

NETZ Engine

Evaluating numerical algorithm

UNIT 10 • INTEREST & FINANCE

EMI Calculator
with Amortisation Schedule

HOW AN EMI IS WORKED OUTREDUCING BALANCE

\begin{gathered} EMI = \frac{P \, i \, (1 + i)^N}{(1 + i)^N - 1} \\ i = \frac{R}{12 \times 100}, \quad N = \text{months} \end{gathered}

1. Monthly RateDivide the yearly rate by 12 and by 100: 9% a year gives

i = 0.0075

2. MonthsTurn the tenure into months: 5 years is

N = 60

3. Each MonthInterest = balance × i. The rest of the EMI reduces the balance.

Step-by-Step Worked Example

HAND-HOLDING TUTORIAL

OUR PROBLEM TO SOLVE

A car loan of ₹5,00,000 is taken at 9% a year for 5 years. Find the EMI, the total interest, and how the first two EMIs are split.

STEP 01 • MONTHLY RATE AND MONTHS

i = \frac{9}{12 \times 100} = 0.0075, \qquad N = 5 \times 12 = 60, \qquad (1.0075)^{60} = 1.565681

STEP 02 • EMI

EMI = \frac{5{,}00{,}000 \times 0.0075 \times 1.565681}{1.565681 - 1} = \frac{5871.30}{0.565681} \approx 10{,}379.18

STEP 03 • TOTAL INTEREST

\text{Total paid} = 10{,}379.18 \times 60 = 6{,}22{,}750.66

\text{Total interest} = 6{,}22{,}750.66 - 5{,}00{,}000 = 1{,}22{,}750.66

STEP 04 • THE FIRST TWO EMIs

\text{Month 1: interest} = 5{,}00{,}000 \times 0.0075 = 3750, \quad \text{principal} = 10{,}379.18 - 3750 = 6629.18

\text{Month 2: interest} = 4{,}93{,}370.82 \times 0.0075 = 3700.28, \quad \text{principal} = 6678.90

The interest part shrinks each month and the principal part grows, while the EMI stays the same.

FINAL CONCLUSION

EMI ≈ ₹10,379.18 for 60 months

EMI \approx 10{,}379.18, \qquad \text{interest} \approx 1{,}22{,}750.66

The calculator below opens on this loan. Add a prepayment of ₹1,00,000 after month 24 to see it finish a year early.

LABORATORY

Interactive EMI Calculator

LABORATORY

EMI Engine

Loan amount PInterest rate R (% a year)TenureTenure is inCurrency

Interest is charged on

Prepayment (optional)

Extra amount paid onceAfter which month?

Common Questions

What is the EMI formula?

EMI = \frac{P\,i\,(1+i)^N}{(1+i)^N - 1}

, where P is the loan,

i

is the monthly rate (yearly rate ÷ 12 ÷ 100) and N is the number of months.

Why is most of the early EMI interest?

Is a flat rate cheaper than a reducing rate?

Does prepaying a loan save money?

Yes. A prepayment goes straight to the principal, so every later month charges less interest. If you keep the same EMI, the loan ends sooner. Check whether your lender charges a prepayment fee first.

PreviousSimple & Compound Interest

Unit 10•47 of 47

EMI Calculator with Amortisation Schedule

Step-by-Step Worked Example

EMI ≈ ₹10,379.18 for 60 months

Interactive EMI Calculator

EMI Engine

Common Questions

NETZ Engine

EMI Calculator with Amortisation Schedule

Step-by-Step Worked Example

EMI ≈ ₹10,379.18 for 60 months

Interactive EMI Calculator

EMI Engine

Common Questions

EMI Calculator
with Amortisation Schedule

EMI Calculator
with Amortisation Schedule