Hello friends & Very good morning!!!
Today we are going to see chapter
Simple Interest which some of us finds very simple chapter but as everything of
this chapter is related or wondering around a single simple formula, namely
P X R X N
SI = ------------------------
100
Suppose “A” received Rs. 500 from B on 10% interest for 2 years then
our parameters becomes
P = Principle = 500
R = Rate % = 10 %
N = Time Period = 2 years
One more thing we missed in this formula is “Rate Calculation
Frequency”, this simply means, “In a total period how many times Rate is
calculated against Principle”
Again in short, as we know in above example rate is calculated per
year. As follows
Before
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at 1st year’s end
|
at 2nd year’s end
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500
|
One Rs. 100 he’s taking Rs. 10, means on Rs. 500 He’ll take Rs. 50,
so total will be Rs. 500+ Rs. 50 = 550
|
One Rs. 100 he’s taking Rs. 10, means on Rs. 500 He’ll take Rs. 50,
so total will be
Rs. 500 + Rs. 50 = 550
|
Note :
|
He(B)’s taking Rs. 10 on Rs. 500 as Rate on Principle once every year
only & considering He has given Rs. 500 to B
|
This means every year he’s taking Rs. 50 as his Rs. 500 usage charge.
Banks does the same but with little complicated formula.
|
But one thing we can say that, we don’t need such complex formula to
calculate Amount. I explain you this in short.
Suppose He’s taking Rs. 50 every year then we need to calculate just
once this number. Thereafter we can multiply with no.of years (&obviously
frequency) to get final interest rate.
Like this
Let
P = 500, R% = 10%, N = 5 Years, A =? &
P = 1500, R% = 10%, N = 7 Years, A =?
1yr Interest
|
2yr
|
3yr
|
4yr
|
5yr
|
6yr
|
7yr
|
|
P = 500
|
50
|
100
|
150
|
200
|
250
|
||
P = 1500
|
150
|
300
|
450
|
600
|
750
|
900
|
1050
|
What we did is this part here…
SI = P X R X N /100
In terms of math, we can say that
SI = R% of P for N years
& we just pre-calculated (R% of P) first then we multiplied by
no.of years (and then frequency)
One more thing in SI is this formula gives only SI but not A (Amount
final). For that we need to add P to SI.
So
A = SI + P
This is the general formula for SI.
I would like to tell one more thing about this is that when we gets
figures in parameters cancelling each other. We can use this formula too. But
large figures tends to large calculations. I was just explaining what inside happens
with SI.
Next we’ll see about frequency this is one of the parameter most of the
exams avoid. Since this is not used in daily practice. I mean no banks allow
lending their money on quarterly or half yearly basis. But still formula is
necessary to thing/ talk about it further.
P x R x N x F
SI = -------------------------
100
This is nothing but the extension of formula, meaning of this F here is
“How many times in a year rate % is calculated on P”
Suppose they calculate it 2 times in a year (means half yearly) then
500 x 10 x (2 x 2)
SI = -------------------------------- = 200
100
A = 500 + 200 = 700
This just doubles the years & nothing else. So, for quarterly calculating
rates, we need to multiply with 4.
One more thing I would like to suggest you here is to read my post on converting
any decimal to % . In this article I have written how one can easily
convert any fraction to percentage. This will great help for you while doing
mind calculations on SI.
Next SI on Daily basis:
Most of the times, not in field of banking but while lending some money
to your friend, we need to charge some interest on him. This interest is
comparatively smaller than what bank takes. Like 3.5%, 1.5%, 2%. But calculated
on daily basis. People think that as R% is small we will have to pay less. But
they don’t see frequency of calculating interest rate. As it is happening 365
times a year we have to multiply by 365 to our SI formula which will be
P x R x N x 365
SI = -------------------------
100
Note: in previous examples and in banks instead of 365 there is 1 only.
I mean if you are popular & people think you are rich then you can also
lend money, and earn good profits.
Next we’ll see other variations of formulas
Other Variations:
We know that
P x R x N
SI = ---------------------
100
For calculating P, the formula will be
SI x 100
P = ---------------------
R x N
Also
SI x 100
P + SI = --------------------- + SI
R
x N
= SI ( 100/RN + 1 ) = A…(1)
This formula is more like CI’s formula, which is
A = P(1 + R/100)N …(2)
Now you can compare both formulas if some years both SI & CI are
given & you are expected to calculate R% or P.
Hope more simple examples on this will be covered in solved examples section
lastly.
Solved Examples:
Q. At what rate per annum will a sum of Rs 3600 becomes Rs
4500 in 10 years at Simple Interest?
Ans: SI= 4500 – 3600 = 900
Since SI = PNR / 100
900 = 3600 *
R * 10 / 100
R = 2.5 %
Q. At what rate will a sum of money becomes double in 16
years at simple interest?
Ans: R= 100 / T
= 100/16
= 6.25 %
Q. At what rate will a sum of money become 6 times in 20
years at simple interest?
Ans: R = 500/T
= 500/20
= 25%
Q. If a certain sum at simple interest amounts to Rs 1260 in
2 years and Rs 1350 in 5 years, find the rate and principle?
Ans: SI for 3 years = 1350 – 1260 = 90
SI for one year = 30
SI for two years = Rs 60
Amount = P + SI
1260 = P + 60
P = 1260 – 60 = Rs. 1200
the principle amount = Rs. 1200
To find out the rate of SI,
SI = PNR
R = SI / (P* N)
= 30 / (1200 *1)
= 2.5 %
Q. What is the capital required to earn a monthly
interest of Rs 600 at 6% per annum?
Ans:
SI = 600 per month
R = 6%
SI = PNR /100
600 * 12 = P * 1 * 6 /100
P = 600 * 12 * 100 / 6 = 1,20,000
Q. A sum of money was put at SI at a certain rate for 2
years. Had it been ut at 1% higher rate, it would have fetched Rs 24 more. Find
the sum.
There are two steps for solving this kinda examples
2 years , Rs 24 more
1 years , 24/ 2, ie 12 more
1 % of P = 12 (since the rate increased by 1%)
Ie p * 1/100 = 12
P = 1200
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