Q.Write the syntax for the following functions :

Imagine you borrow money from a bank. The bank wants its principal back, plus interest for the time it stayed with you. You, on the other hand, want to pay in equal, predictable chunks — the same amount every month — so you can budget. The PMT function answers exactly one question: what is that equal chunk?

The word "PMT" is short for payment. It is a spreadsheet function (Excel, Google Sheets, LibreOffice) that returns the constant periodic instalment needed to fully repay a loan — principal plus all interest — over a fixed number of periods, at a fixed interest rate per period.

The intuition first

Think about what a single instalment actually does. When you pay ₹10,000 in month one, part of it covers the interest that has already piled up on your outstanding balance, and the rest chips away at the principal. Next month the balance is smaller, so the interest is smaller, so a bigger slice of your same ₹10,000 goes to principal. The instalment stays flat; only its composition shifts.

That is the whole idea of an amortising loan. PMT is the number that makes this process end exactly at zero after the last period. Pay a rupee less each month and you never finish; pay a rupee more and you overpay. PMT finds the precise balance point.

The precise statement

For a loan of present value $PV$ (the amount borrowed today), repaid over $n$ periods at an interest rate $i$ per period, the payment is:

Each symbol, carefully:

• $PV$ — the principal, i.e. the loan amount today. In finance this is a present value, which is why the function calls it $PV$.
• $i$ — the interest rate per period, as a decimal. A 12% annual rate paid monthly is $i = 0.12/12 = 0.01$ per month. This is the single most common place students go wrong.
• $n$ — the total number of periods, not years. A 5-year loan paid monthly has $n = 60$.
• $PMT$ — the equal payment made each period. It comes out negative in a spreadsheet if you enter $PV$ as positive, because the payment is cash leaving your pocket.

The formula assumes payments are made at the end of each period (an ordinary annuity), which is how almost all loans work.

Reading the formula

The numerator $PV \cdot i$ is the interest owed on the full principal in the very first period. If you only ever paid interest and never touched the principal, that would be your payment forever — an interest-only loan.

The denominator $1 - (1+i)^{-n}$ is the correction that forces the principal to be repaid too. Notice $(1+i)^{-n}$ is the present value of ₹1 received $n$ periods from now — a small number. So the denominator is a bit less than 1, which inflates the payment above the pure-interest figure. The longer the loan (larger $n$), the smaller $(1+i)^{-n}$, the closer the denominator is to 1, and the smaller each payment — but the more total interest you pay overall.

A worked example

A loan of ₹5,00,000 at 12% per annum, repaid monthly over 5 years.

• $PV = 500000$
• $i = 0.12/12 = 0.01$
• $n = 5 \times 12 = 60$

$PMT = \frac{500000 \times 0.01}{1 - (1.01)^{-60}} = \frac{5000}{1 - 0.55045} = \frac{5000}{0.44955} \approx 11122$ …