What is Interest ?


What is interest ?

A bank earns money from the interest it receives on loans and other assets, and it pays out money to customers who make deposits into interest-bearing accounts. The difference between these two is known as the spread. It is important for both the customers and the employees to have a better insight into the interest. 

According to Wikipedia "Interest, in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate."

However, the rate of interest for both loans and deposits depends on several factors:- 
  • Type of loans or deposits
  • Amount of expected inflation
  • Length of time money is lent or deposited
  • Inflation
Basically, there are two types of interest:-
  1. Simple Interest 
  2. Compound Interest
Simple Interest  

'Simple' interest or 'flat-rate' interest is the amount of interest paid each year in a fixed percentage of the amount borrowed or lent at the start. The formula for calculating simple interest is as follows:
Interest = Principal * Rate x Time ( PRT)

Where,
'Interest' is the total amount of interest paid,
'Principal' is the amount lent or borrowed (This amount remains unchanged during the period of the
loan.)
'Rate' is the percentage of the principal charged as interest each year.

Illustration
A student purchases a computer by obtaining a loan on simple interest. The computer costs Rs. 1,500
and the interest rate on the loan is 12 percent. If, the loan is to be paid back in weekly installments over two years, calculate:
  1. The amount of interest paid over the two years,
  2. The total amount to be paid back,
  3. The weekly payment amount.
Given: Principal: 'P' = Rs. 1,500, Interest rate: 'R' = 12% = 0.12, Repayment time: T = 2 years
Part 1: Find the amount of interest paid.
Interest: T = PRT
= 1,500x0.12x2 =
Rs. 360
Part 2: Find the total amount to be paid back.
Total repayments = Principal + Interest = Rs.
1,500+ Rs. 360 = Rs. 1,860

Part 3: Calculate the weekly payment amount
Weekly payment amount = Total repayments / Loan period, T, in weeks
                                         =  Rs. 1,860 / 2x52
                                         = Rs. 17.88 per week

Compound Interest 

In the simple interest formula, it is presumed that interest is charged only once during the given period. Against this, if the interest is charged more than once during the period and the interest is reinvested, we need to compound the interest. Compound interest is paid on the original principal and accumulated part of interest. For an illustration
P = Principal (Initial amount you borrowed or deposited) r = Annual rate of interest (per cent) n =
Number of year the amount of deposit
A = Amount of money accumulated after n year including interest.
When interest is compounded once in a year,
A = P(1 +r)^n

Illustration-1
Mohan invested Rs. 5,000 in a mutual fund with the interest rate of 4.8%. How much interest would he
earn after 2 years?
Answer,
P = Rs. 5,000
r = 4.8%
t = 2 years
I = P x r t
I = (Rs. 5,000) (4.8%) (2) = Rs. 480
Hence, Mohan would earn Rs. 480 after 2 years.

Illustration-2

Jhangir has one saving account with an interest rate of 3.3%, and one money market account with an interest rate of 5.1%, in a bank. If he deposits Rs. 1,200 to the savings account and Rs. 1,800 to the money market account, how much money will he have after 6 years?
Answer,
Savings account:
P=Rs. 1,200
r = 3.3% 
A = P x ( | +rt)
A = (Rs. l,200)[l +(3.3%)(6)]
= (Rs. l,200)( 1.198)
= Rs. 1,437.60
Money market account:
P=Rs. 1,800 r
= 5.1% t = 6
A = P x ( i+ r t ) A = (Rs. 1,800) [1+(5.1%) (6)] = (Rs.
1,800.00) (1.306) = Rs. 2,350.80 Total amount = Rs.
1,437.60 + Rs. 2,350.80 = Rs. 3,788.40
Hence, Jhangir will have Rs. 3,788.40 after 6 years.

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