(a) Calculate the EMI under 'Flat Rate System' for a loan of ₹ 5,00,000 with 10% annual interest rate for 5 ye

Question

Q. (a) Calculate the EMI under 'Flat Rate System' for a loan of ₹ 5,00,000 with 10% annual interest rate for 5 years.

(OR)

(b) A machine costing ₹ 2,00,000 has effective life of 7 years and its scrap value is ₹ 30,000. What amount should the company put into a sinking fund earning 5% p.a., so that it can replace the machine after its usual life ? Assume that a new machine will cost ₹ 3,00,000 after 7 years. [Given that :

(1 \cdot 05)^7 = 1 \cdot 407

]

CBSECBSE Class XII Board 2022Subjective· 4mImportance★★★★★

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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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Total interest $=$ ₹2,50,000, total due $=$ ₹7,50,000 over 60 months $\Rightarrow$ EMI $=$ ₹12,500.
Target $=$ ₹2,70,000 (new cost $-$ scrap); annual deposit $=270000\times\dfrac{0.05}{1.407-1}\approx$ ₹33,169.53.

I=P\cdot r\cdot t

Part (a) — Flat Rate EMI

Given $P=5{,}00{,}000$ , $r=10\%=0.10$ p.a., $t=5$ years.
Total (flat) interest: $I=P\cdot r\cdot t=500000\times 0.10\times 5 = 250000$ .
Total amount repayable: $P+I=500000+250000=750000$ .
Number of monthly instalments: $12\times 5 = 60$ .
EMI $=\dfrac{750000}{60}=12500$ .

Part (b) — Sinking Fund …

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Q.(a) Calculate the EMI under 'Flat Rate System' for a loan of ₹ 5,00,000 with 10% annual interest rate for 5 years.

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