Independence Day - 77INDIA

# Simple Interest and Compound Interest for Bankers

If you are aiming to become a banker, then these two fellows should be your best buddies – SI and CI!

SI and CI are fairly simple concepts and their calculations are simple too – but somehow I've seen most of my banking–students– friends to have a mental block with regards to these topics.

Question(s) from these chapters is a must – so it only makes sense to master this chapter once and for all and never forget it!

### 1. What is simple/compound interest?

When we deposit our money with the bank or with anyone, we give away our money for the time being. That is we do not have that amount with us in our hands anymore and hence can not make use of it.

That money is used by somebody else – the banks for giving loans to other – and thus our money is utilized to earn profits by the banks (they charge interests on the loans given by them).

Thus our money, which we cannot utilize as of now, because it is with somebody else and giving them benefits, is the underlying concept of SI and CI.

SI and CI are our compensation for giving our money for a time being to be used by others. Thus Interest = our compensation!

### 2. Simple Interest?

Is a type of interest calculation, where interest is calculated on a particular amount, known as the principal amount, for an entire period put together. Simple enough?

#### Basic formulae and what we can understand from them:

(i) Interest Amount  = Principal x Time in years x Rate(p.a.)%
or,
I = P x T x (R/100)

(ii) Total Amount received at the time of maturity = Principal + Interest Amount
or, A = P + I

(iii) Time in years can be derived as,
T = Total Interest/Interest on the principal for 1 year

if you look carefully, this is nothing but using opposite of unitary method to

find out the number of years.

Note: Time is always in years. If it is not…refer to point (v)

(iv) Rate can be derived as,
R= (I x 100)/(P x T), is nothing but the original formula to find R.

Note: Rate will always be per annum, i.e., denoted as ‘p.a.’ or ‘p.c.p.a’. If it is
not…refer point (v)

(v) Percent per annum is how a rate is normally given, and time is given in years; our SI formula is also based on this premises.

So, rate – per annum
time – in years, (remember this!)

But suppose if you’re given time to be 6 months – what do you do? You will convert it into years, by dividing it with 12 (cuz 12 months make a year!)

therefore, 6 moths = 6/12 = ½ year.
36 months = 36/12 = 3 years
52 months = 13/3 years, when you get years in fraction do not solve them, keep
them in their fractional form and solve the formula, you’ll definitely be able to
cancel them off!

Now, if you are given monthly rate instead of yearly rate, say 0.8% per month, what do you do to make it an annual rate? You will multiply it with 12 (cuz there are 12 months!) to make it the yearly rate!

therefore, 0.8 x 12 = 9.6% p.a. and now you can use it in your original formula!

if it is 2% per quarter – then – 2 x 4 = 8% per annum (cuz there are 4 quarter in a year)

if it is 5% per six months/semi annual rate/half yearly rate – 5 x 2 = 10% per annum!

I hope this much is clear to you.

### 3. Compound Interest?

Here the interest is calculated for a specified ‘unit of time’; say monthly/half yearly/quarterly/yearly.

Since, there is the ‘unit of time’, the interest on principal for the ‘unit of time’ accrued is taken and added to the original principal and this amount becomes the principal for the next unit of time/interval.

Example: Your original principal is Rs.100 and Interest rate is 10% per annum compounded annually.

 Amount (principal) Interest amount for the period 100 10 110 (100 + 10) 11 121 (110 + 11) 12.1 133.1 (121 + 12.1) 13.31  … and so on…

Formula for amount, where interest is compounded annually for ‘n’ years is:

Amount = Principal x [1 + (R/100)]n

this is the basic formula, where when interest is compounded monthly/half yearly/quarterly we do two things -
(i) multiply n with 12/2/4 respectively, and
(ii) divide rate with 12/2/4 respectively.

thus resultant formulae become – P x [1 + (R/12 x 100)]12n for monthly compounding,
P x [1 + (R/2 x 100)]2n for semi-annual compounding, and
P x [1 + (R/4 x 100)]4n for quarterly compounding.

### 4. Relation between SI and CIs:

The difference between SI and CI, where principal and rate of interest are same – of say 2 years will be given by:

P x (R/100)2, and so on…the power will change as per number of years…

### 5. General guidelines for Data Sufficiency:

Know the formulae and know which figures are needed to give you the required result – for example if they give in the Principal and rate and Interest amount in one statement, you can find out the number of years.

Using the number of years, the second statement may ask you to find the compound interest on the same amount!

Presence of mind and practice will make you very confident in SI and CI data sufficiency questions.

Your aim should be to solve DS questions just by looking at what the available information. Yes it is very much achievable.

That is all for today. Keep the feedback coming in.