Class 10: Banking – Lecture Notes

$\displaystyle \textbf{What is Banking?}$
$\displaystyle \text{Banking is the business of receiving money from depositors, safeguarding it, and lending it}$
$\displaystyle \text{to individuals or businesses.}$
$\displaystyle \text{Thus, banks are institutions that accept deposits and provide loans.}$
$\displaystyle \text{Depositors earn interest on their deposits, while borrowers pay interest on loans.}$
$\displaystyle \text{The difference between these, after deducting operational costs, forms the bank's earnings.}$
$\displaystyle \text{Bank's Earnings = Interest Earned - Interest Paid - Operational Cost}$
$\displaystyle \text{A banking licence is required to start banking operations.}$
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$\displaystyle \textbf{Types of Accounts}$
$\displaystyle \text{For this course, we shall study the following types of accounts:}$
$\displaystyle \text{1. Savings Bank Account}$
$\displaystyle \text{2. Recurring Deposit Account}$
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$\displaystyle \textbf{Savings Bank Account}$
$\displaystyle \text{In a Savings Bank Account, money can be deposited or withdrawn at any time.}$
$\displaystyle \text{The account holder earns interest, which may vary with market conditions.}$
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$\displaystyle \textbf{Calculation of Interest}$
$\displaystyle \text{Although banks now calculate interest daily, for this syllabus it is calculated monthly.}$
$\displaystyle \text{Step 1: Find the minimum balance from the }10^{\text{th}}\text{ day to the last day of each month.}$
$\displaystyle \text{This minimum balance is treated as the principal for that month.}$
$\displaystyle \text{Step 2: Add the monthly principal amounts for the required period.}$
$\displaystyle \text{Step 3: Calculate Simple Interest on this total principal for one month at the given rate.}$
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$\displaystyle \textbf{Recurring Deposit Account}$
$\displaystyle \text{In a Recurring Deposit (R.D.) Account, a fixed amount is deposited every month for a fixed}$
$\displaystyle \text{period chosen by the depositor.}$
$\displaystyle \text{At maturity, the depositor receives the total deposits along with interest compounded quarterly.}$
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$\displaystyle \textbf{Maturity Value}$
$\displaystyle \text{Maturity Value = Total Sum Deposited + Interest Earned}$
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$\displaystyle \text{If }P\text{ is deposited every month for }n\text{ months at }r\%\text{ per annum, then}$
$\displaystyle I=P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
$\displaystyle \text{Total Sum Deposited}=P\times n$
$\displaystyle \text{Maturity Value}=P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
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$\displaystyle \textbf{Proof}$
$\displaystyle \text{Amount of the first monthly deposit after }n\text{ months}$
$\displaystyle =P+P\times\frac{r}{100}\times\frac{n}{12}$
$\displaystyle \text{Amount of the second monthly deposit after }(n-1)\text{ months}$
$\displaystyle =P+P\times\frac{r}{100}\times\frac{n-1}{12}$
$\displaystyle \text{Amount of the third monthly deposit after }(n-2)\text{ months}$
$\displaystyle =P+P\times\frac{r}{100}\times\frac{n-2}{12}$
$\displaystyle \cdots$
$\displaystyle \text{Amount of the }(n-1)^{\text{th}}\text{ monthly deposit after }2\text{ months}$
$\displaystyle =P+P\times\frac{r}{100}\times\frac{2}{12}$
$\displaystyle \text{Amount of the }n^{\text{th}}\text{ monthly deposit after }1\text{ month}$
$\displaystyle =P+P\times\frac{r}{100}\times\frac{1}{12}$
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$\displaystyle \therefore\ \text{Maturity Value}=P\times n+P\times\frac{r}{100}\left(\frac{n}{12}+\frac{n-1}{12}+\frac{n-2}{12}+\cdots+\frac{2}{12}+\frac{1}{12}\right)$
$\displaystyle =P\times n+P\times\frac{r}{100\times12}\left[n+(n-1)+(n-2)+\cdots+2+1\right]$
$\displaystyle =P\times n+P\times\frac{n(n+1)}{2\times12}\times\frac{r}{100}$
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