Mr. M borrowed ₹10,00,000 from a bank to purchase a house and decided to repay by monthly equal instalments in 10 years. The bank charges interest at 9% compounded monthly. The bank calculated his EMI as ₹12,668. Find the principal and interest paid in first year? (Given $a_{\ove

Question

Mr. M borrowed ₹10,00,000 from a bank to purchase a house and decided to repay by monthly equal instalments in 10 years. The bank charges interest at 9% compounded monthly. The bank calculated his EMI as ₹12,668. Find the principal and interest paid in first year? (Given $a_{\overline{108}|0.0075} = 73.83916$)

Accepted Answer

> [!TLDR]
> After 12 payments, the balance is the present value of the remaining 108 EMIs: $12{,}668	imes a_{\overline{108}|0.0075}=12{,}668	imes73.83916=₹9{,}35{,}395$. So in the first year the **principal repaid is ₹64,605** and the **interest paid is ₹87,411**.

The EMI is ₹12,668 for 120 months at 9% p.a. compounded monthly ($i=0.0075$). The outstanding balance at any point equals the present value of the payments still to be made.

1. **Balance after 12 payments** (108 EMIs remain):
$$12{,}668	imes a_{\overline{108}|0.0075}=12{,}668	imes73.83916=₹9{,}35{,}395.$$
2. **Principal repaid in the first year.**
$$10{,}00{,}000-9{,}35{,}395=₹64{,}605.$$
3. **Interest paid in the first year** = total paid in 12 months minus principal repaid: …

Concept understanding — Flat Interest Rate EMI

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Step-by-step breakdown

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