1.1 Foundational Financial Terminology
In commercial transactions involving loans and savings, five core mathematical variables interact:
| Term (English / Bengali) | Symbol | Mathematical Definition | Standard Unit |
|---|---|---|---|
| Principal (আসল বা মূলধন) | $P$ | The initial sum of money borrowed, lent, or deposited. | Rupees (₹) |
| Rate of Interest (বার্ষিক সুদের হার) | $R$ or $r\%$ | The interest accrued on ₹100 for a duration of 1 year. | Percent per annum (% p.a.) |
| Time (সময়) | $T$ or $t$ | The total duration for which the principal is utilized. | Years (বছর) |
| Simple Interest (মোট সরল সুদ) | $I$ | The uniform charge paid exclusively on the original principal. | Rupees (₹) |
| Amount (সবৃদ্ধিমূল বা সুদাসল) | $A$ | Total return: Principal + Total Interest ($A = P + I$). | Rupees (₹) |
1.2 Derivation of the Master Formula
By definition, the interest on ₹100 for 1 year is ₹$R$.
Using the unitary method:
Interest on ₹1 for 1 year = ₹$ rac{R}{100}$
Interest on ₹$P$ for 1 year = ₹$ rac{P imes R}{100}$
Interest on ₹$P$ for $T$ years = ₹$ rac{P imes R imes T}{100}$
The Master Formula: $I = rac{P \cdot R \cdot T}{100}$
Total Amount formula in terms of $P, R, T$:
$A = P + I = P + rac{PRT}{100} = P\left(1 + rac{RT}{100}
ight) = rac{P(100 + RT)}{100}$