What is banking?

  • Business of receiving money from depositors (or account holders), safe guarding and lending money to business or individuals is called banking.
  • Therefore Banks are institutions which carry out the business of taking deposits and lending money.
  • When people deposit money, based on the scheme under which they deposit money, they get a return on their money.
  • Similarly, when the bank lends the money to people or business, banks charge a rate of interest on the amount of money given our.

The difference in the two is what the bank earns adjusted to their operational costs. In a very simple way we could say:

Banks \ Earnings = Earning \ on \ Money \ Invested - Interest \ paid \ to \ account \ holders - Operational \ cost

Off-course, banks have to take a banking license to start bank operations.

Types of Accounts: There are many types of accounts but from a course perspective, we will look at the following accounts:

  1. Savings Bank Account
  2. Recurring Deposit Accounts

Saving Bank Account

A person can deposit and withdraw money at will. The person gets a certain interest on the deposits, which could change with change in market conditions.

How do we calculate the interest on the deposit?

Now a days, because of the powerful computers, the banks are able to calculate interest on a day to day basis. However, for our syllabus, we would calculate interest on a monthly basis. The concept is the same though. Here is how we will do it.

  1. Find the minimum balance on the 10^{th} day  and up to the last day of each month. This minimum balance becomes the principal of the month.
  2. Add all such Principal amounts obtained for different months of a particular period in consideration.
  3. Now calculate the simple interest on the Principal obtained in Step 2 for one month at the prevailing rate of interest at that time.

Recurring Deposit Account

In this type of deposits, the account holder deposits a specified amount in the account every month for a fixed period of time. It could be three months to say 10 years. The time period is decided by the bank.

At the expiry of the period, the person gets a lump sum of money which includes the money that was deposited and the interest (compounded quarterly) that the money has earned over a period of time.

The formula that we use for calculating the maturity value of the recurring deposit is:

Maturity \ Amount = Total \ Sum \ Deposited + Interest \ Earned  

If P is deposited every month in the bank for n months and  r\% is the rate of interest per year, then

I=P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}

Total \ Sum \ Deposited = P \times n  

Maturity \ Value = P \times n + P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}

Proof: If P is deposited every month in the bank for n months and  r\% is the rate of interest per year, then

Maturity amount for P deposited in the 1^{st} month after n months

= P + P \times \frac{r}{100} \times \frac{n}{12}

Maturity amount for P deposited in the 2^{nd} month after (n-1) months

= P + P \times \frac{r}{100} \times \frac{(n-1)}{12}

Maturity amount for P deposited in the 3^{rd} month after (n-1) months

= P + P \times \frac{r}{100} \times \frac{(n-2)}{12}

\cdots

Maturity amount for P deposited in the (n-1)^{th} month after (n-1) months

= P + P \times \frac{r}{100} \times \frac{2}{12}

Maturity amount for P deposited in the (n)^{th} month after (n-1) months

= P + P \times \frac{r}{100} \times \frac{1}{12}

Therefore

Maturity amount = P \times n + P \frac{r}{100} \Big(  \frac{n}{12} + \frac{n-1}{12} + \frac{n-2}{12} + \cdots + \frac{2}{12} + \frac{1}{12} \Big)

= P \times n + P \frac{r}{100 \times 12 } \Big( n + (n-1) + (n-2) + \cdots + 2 + 1 \Big)

= P \times n + P \frac{n(n+1)}{2 \times 12} \frac{r}{100}