Ramesh borrowed a home loan amount of ₹ 7,00,000 from a bank at an interest of 12% per annum for 30 years, to

Question

Q. Ramesh borrowed a home loan amount of ₹ 7,00,000 from a bank at an interest of 12% per annum for 30 years, to be paid in monthly installments. Based on the above information, answer the following questions :

(i) Write the formula for calculating EMI by reducing balance method.

(ii) Write the values of P, i and n respectively.

(iii) Find the EMI. [Use

(1.01)^{-360} = 0.02781668

]

(OR)

(iii) If the loan is to be returned in 20 years, find EMI. [Use

(1.01)^{-240} = 0.09180584

]

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Concept understanding — Flat Interest Rate EMI

Flat Interest Rate EMI — From Intuition to Precision

Imagine you borrow ₹1,00,000 from a bank for 1 year. The bank says: "We charge 12% interest per year, flat." What does "flat" mean here?

The intuition: The bank calculates the total interest on the entire original loan amount for the full loan tenure, regardless of how much you've already repaid. You pay interest on the full ₹1,00,000 for the whole year — even though you're paying back the principal bit by bit each month.

Step-by-step breakdown

Let’s take a concrete example:

Loan amount (P): ₹1,00,000
Annual flat interest rate (R): 12%
Tenure (N): 1 year (12 months)

Step 1: Total interest for the year

Interest = Principal × Rate × Time

= ₹1,00,000 × (12/100) × 1 = ₹12,000

Step 2: Total amount to repay

Principal + Interest = ₹1,00,000 + ₹12,000 = ₹1,12,000

Step 3: Monthly EMI

EMI = Total amount ÷ Number of months

= ₹1,12,000 ÷ 12 = ₹9,333.33 per month

Note

Every month you pay ₹9,333.33. The interest portion in each EMI is not decreasing — it's a fixed ₹1,000 per month (₹12,000 ÷ 12). The principal repaid each month is also fixed: ₹8,333.33.

The precise formula

\text{EMI}_{\text{flat}} = \frac{P + (P \times R \times N)}{N}

Where:

$P$ = original loan principal
$R$ = annual flat interest rate (as a decimal, e.g., 0.12 for 12%)
$N$ = loan tenure in months (or years, as long as consistent)

Alternatively, in a cleaner form:

\text{EMI}_{\text{flat}} = \frac{P}{N} + \frac{P \times R}{12}

The first term is the fixed principal repayment per month. The second term is the fixed monthly interest.

Why "flat" is important — and a warning

Watch out

A flat interest rate looks lower than the equivalent reducing-balance rate, but it's actually more expensive.

In our example, 12% flat is equivalent to about 21.5% reducing-balance interest — nearly double. …

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Reducing-balance EMI $= \tfrac{Pi}{1-(1+i)^{-n}}$ . With $P=700000,\ i=0.01$ : for $n=360$ , EMI $= \tfrac{7000}{1-0.02781668} \approx ₹7{,}200.29$ ; for $n=240$ , EMI $= \tfrac{7000}{1-0.09180584} \approx ₹7{,}707.60$ .

\text{EMI} = \dfrac{P\,i}{1 - (1+i)^{-n}} = \dfrac{P\,i\,(1+i)^{n}}{(1+i)^{n} - 1}

Formula. $\text{EMI} = \dfrac{P\,i}{1 - (1+i)^{-n}}$ .
Values. $P = ₹7{,}00{,}000$ ; monthly rate $i = \dfrac{12}{12\times100} = \dfrac{12}{1200} = 0.01$ ; $n = 12 \times 30 = 360$ months.
EMI for 30 years.

Numerator: $P\,i = 700000 \times 0.01 = 7000$ .
Denominator: $1 - (1.01)^{-360} = 1 - 0.02781668 = 0.97218332$ .
$\text{EMI} = \dfrac{7000}{0.97218332} \approx ₹7{,}200.29$ . …

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Q.Ramesh borrowed a home loan amount of ₹ 7,00,000 from a bank at an interest of 12% per annum for 30 years, to be paid in monthly installments. Based on the above information, answer the following questions :

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