JAIIB AFB Unit 1 Calculation of Interest (Part 1)

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.

Formula for calculating simple interest :

Interest = Principal x Rate x Time (PRT), where:

'Interest' is the total amount of interest paid
'Principal' is the amount lent or borrowed
'Rate' is the percentage of the principal charged as interest each year.
'Time' is the time in years of the loan.

Example

Principal: 'P' = Rs. 50,000, Interest rate: 'R' = 10% = 0.10, Repayment time: T = 3 years. Find the amount of interest paid.

Interest = PRT
= 50,000x0.10x3
= Rs. 15,000/-

Compound Interest

Compound interest is paid on the original principal and accumulated part of interest.

Formula for calculating compound interest :

P = A(1 +r/n)^nt,   where

P = the principal
A = the amount deposited
r = the rate (expressed as fraction, e.g. 6 per cent = 0.06)
n = number of times per year that interest is compounded
t = number of years invested

Frequently compounding of Interest. If the interest is compounded :
Annually = P (1 + r)
Quarterly = P (1 + r/4)⁴
Monthly = P (1 + r/12)¹²

Example

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years. Then
30000(1+7/100)ⁿ = 34347
(107/100)ⁿ = 34347/30000
(107/100)ⁿ = 11449/10000
(107/100)ⁿ = (107/100)²
n = 2 years.

The Rule of 72

Allows you to determine the number of years before your money doubles whether in debt or investment. Divide the number 72 by the percentage rate.

EQUATED MONTHLY INSTALMENTS (EMIs)

Equated Monthly Installment (EMI) refers to the monthly payment a borrower makes on his loan. Though it is a combination of interest payment and principal repayment, the total monthly amount is calculated in such a way that it remains constant all through the repayment tenure. In Equated Monthly Installments (EMIs), the principal and the interest thereon is repaid through equal monthly installment over the fixed tenure of the loan. The benefit of an EMI for borrowers is that they know precisely how much money they will need to pay toward their loan each month, making the personal budgeting process easier.

Formula

E = P×r×(1 + r)n/((1 + r)n - 1)

• E is EMI
• P is Principle Loan Amount
• r is rate of interest calculated in monthly basis it should be = Rate of Annual interest/12/100
• if its 10% annual ,then its 10/12/100=0.00833
• n is tenure in number of months

Example

For 100000 at 10% annual interest for a period of 12 months, it comes  to :

100000*0.00833*(1 + 0.00833)12/((1 + 0.00833)12 - 1) = 8792