In the year 2010, Mr. Aggarwal took a home loan of ₹ 30,00,000 from State Bank of India at 7·5\% p.a. compound

Question

7\cdot5\%

(i) Determine the EMI. [1]

(ii) Find the principal paid by Mr. Aggarwal in the

150^{th}

instalment. [1]

(iii)

(a) Find the total interest paid by Mr. Aggarwal. [2]

(OR)

(iii)

(b) How much was paid by Mr. Aggarwal to repay the entire amount of home loan ? [2] [Use

(1\cdot00625)^{240} = 4\cdot4608;\ (1\cdot00625)^{91} = 1\cdot7629

]

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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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EMI $\approx$ ₹24,167.82; $150^{\text{th}}$ principal $\approx$ ₹13,709; total interest $\approx$ ₹28.0 lakh; total repaid $\approx$ ₹58.0 lakh.

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

$P=\text{₹}30{,}00{,}000$ ; $i=\dfrac{7.5\%}{12}=0.625\%=0.00625$ ; $n=20\times12=240.$ Given $(1.00625)^{240}=4.4608.$

(i) EMI

2. $\text{EMI}=\dfrac{3000000\times0.00625\times4.4608}{4.4608-1}=\dfrac{18750\times4.4608}{3.4608}=\dfrac{83640}{3.4608}\approx \text{₹}24{,}167.82.$

(ii) Principal in the $150^{\text{th}}$ instalment

3. Remaining instalments after the $149^{\text{th}}$ : $n-k+1=240-150+1=91.$

4. Principal part $=\text{EMI}\cdot(1.00625)^{-91}=\dfrac{24167.82}{1.7629}\approx \text{₹}13{,}709.$

(iii)(a) Total interest …

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Q.In the year 2010, Mr. Aggarwal took a home loan of ₹ 30,00,000 from State Bank of India at 7⋅5%7\cdot5\%7⋅5% p.a. compounded monthly for 20 years. Based on the above information, answer the following questions :

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Q.In the year 2010, Mr. Aggarwal took a home loan of ₹ 30,00,000 from State Bank of India at $7\cdot5\%$ p.a. compounded monthly for 20 years. Based on the above information, answer the following questions :

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