**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:

- Savings Bank Account
- 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.

- Find the minimum balance on the day and up to the last day of each month. This minimum balance becomes the principal of the month.
- Add all such Principal amounts obtained for different months of a particular period in consideration.
- 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 is deposited every month in the bank for months and is the rate of interest per year, then

Total Sum Deposited

Maturity Value

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

Maturity amount for deposited in the month after months

Maturity amount for deposited in the month after months

Maturity amount for deposited in the month after months

Maturity amount for deposited in the month after months

Maturity amount for deposited in the month after months

Therefore

Maturity amount

how n(n+1)/2*12 comes can you explain.

I have added the proof in the lecture notes. Please refer to it.