2. Objectives :
Recapitulation of What is Interest?, Common terms used in Simple Interest(C.I. also)
Types of Interest
Simple Interest -Definition, Formulae,& it’s explanation
Compound Interest- ~Definition
~Difference between Simple Interest & Compound Interest
~Deducing it’s formula
~Calculating Compound Interest of rate Compounded Half-yearly
~Applications of Compound Interest Formula
After understanding it’s concept, solving Questions
3. What is Interest?
When we borrow money from, or use somebody else’s money, we have to
often pay a charge to him. This amount of money is paid back to the lender
according to the original amount borrowed.
This is sometimes known as the cost of Money which doesn’t belong to you,
but you have used it.
This extra amount is called ‘INTEREST’.
Interest is the extra money paid by institutions like banks or post office on
money deposited with them. Interest is also paid by people when they
borrow money. We already know how to calculate SIMPLE INTEREST.
Let’s quickly manipulate some common terms used in case of SIMPLE
INTEREST (and COMPOUND INTEREST).
1. The original Amount borrowed is known as ‘PRINCIPAL’ or ‘CAPITAL’ in different-different
situations.
1. AMOUNT-The sum of both the ‘Principal’ & ‘Interest’.
5. Simple Interest Formulae
Money Deposited Principal
Additional Money paid
over principal
Interest
Amount = Principal + Interest
𝑃 ∗ 𝑇 ∗ 𝑅
100
Simple Interest =
Here, P=Principal T= Time(Years) and R = Rate of Interest
Using this formulae we can find the other components such as the Principal,
Time and Rate of Interest.
6. Simple Interest Example:
Q. Arun took a loan of ₹1400 with simple interest for as many years as the rate
of Interest. If he paid ₹686 as interest at the end of the loan period, what
was the rate of interest?
Explanation: Given that T = R = x
𝑃 ∗ 𝑇 ∗ 𝑅
100
𝑆𝐼 =
⇒ 686 =
1400 ∗ 𝑥 ∗ 𝑥
100
⇒ 68600 = 1400𝑥2
⇒ 𝑥2 =
68,600
1400
⇒ 𝑥2 = 49
⇒ 𝑥 = 49
⇒ 𝑥 = 7
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒄𝒐𝒓𝒓𝒆𝒄𝒕 𝒂𝒏𝒔𝒘𝒆𝒓 = 𝟕%
7. A Question~
A sum fetched a total simple interest of ₹929.20 at the rate of 8% per annum in 5
years. What is the sum?
Answer:
𝑆. 𝐼. =
𝑃 ∗ 𝑅 ∗ 𝑇
100
₹929.20 =
𝑃 ∗8 ∗5
100
₹92920 = 𝑃 ∗ 40
𝑃 =
₹92920
40
𝑃 = ₹2323
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 = ₹2323
𝑆𝑜 𝑠𝑢𝑚 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 + 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
Sum/Amount = ₹2323 + ₹929.20
= ₹3252.2
8. Compound Interest
Some of its applications are:
1) Increase or decrease in population.
2) The growth of bacteria.
3) Rise or Depreciation in the value of an item.
Compound interest is the interest calculated on the principal and the
interest accumulated over the previous period. It is different from
the simple interest where interest is not added to the principal while
calculating the interest during the next period. Compound interest
finds its usage in most of the transactions in the banking and
finance sectors and also in other areas as well.
10. Steps:
1.Find the simple interest (S.I.) for one year.
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑦𝑒𝑎𝑟 𝑏𝑒 𝑃1. 𝐻𝑒𝑟𝑒 𝑃1 = ₹20,000.
𝑆𝐼1 = 𝑆𝐼 𝑎𝑡 8% 𝑝. 𝑎. 𝑓𝑜𝑟 𝑓𝑖𝑠𝑡 𝑦𝑒𝑎𝑟 = ₹
20000 ∗ 8
100
= ₹1,600
2.Now,find the amount which will be paid or received. This becomes the principal for the
next year.
𝐴𝑚𝑜𝑢𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 1𝑠𝑡 𝑦𝑒𝑎𝑟 = 𝑃1
+ 𝑆𝐼1
= ₹20,000 +₹1,600
= ₹21,600 = 𝑃2
(𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙𝑓𝑜𝑟 2𝑛𝑑 𝑦𝑒𝑎𝑟)
3.Now,find the interest for another year.
𝑆𝐼2 = 𝑆𝐼 𝑎𝑡 8% 𝑝𝑒𝑟 𝑎𝑛𝑛𝑢𝑚 𝑓𝑜𝑟 2𝑛𝑑 𝑦𝑒𝑎𝑟 =
₹ 21,600 ∗ 8
100
= ₹1,728
11. 4.Find the total amount which has to paid/received at the end of the second year.
𝐴𝑚𝑜𝑢𝑛𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 2𝑛𝑑 𝑦𝑒𝑎𝑟 = 𝑃2 + 𝑆𝐼2(𝑨𝒔 𝒂𝒎𝒐𝒖𝒏𝒕 = 𝑷𝒓𝒊𝒏𝒄𝒊𝒑𝒂𝒍 + 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕)
= ₹21,600 + ₹1728(𝑆𝐼 𝑜𝑓 𝑠𝑒𝑐𝑜𝑛𝑑 𝑦𝑒𝑎𝑟)
= ₹23,328
𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐺𝑖𝑣𝑒𝑛 = 𝑺. 𝑰. 𝒐𝒇 𝟏𝒔𝒕 𝒚𝒆𝒂𝒓 + 𝑺. 𝑰. 𝒐𝒇 𝟐𝒏𝒅 𝒚𝒆𝒂𝒓
= S. I.1
+S. I.2
= ₹1600 + ₹1728 =
= ₹3328{𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡}
Now, let us find the S.I. for 2 years, in order to understand the difference between
Simple Interest and Compound Interest.
𝑆. 𝐼. 𝑓𝑜𝑟 2𝑦𝑒𝑎𝑟𝑠 =
𝑃 ∗ 𝑅 ∗ 𝑇
100
=
₹ 20,000 ∗8∗2
100
= ₹3,200
Thus we conclude that Heena would have to pay ₹128 more in case of
Compound Interest than in case of Simple Interest.
12. Q.A sum of ₹100 𝑖𝑠 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑 𝑏𝑦 𝑅𝑒𝑒𝑛𝑎 𝑓𝑜𝑟 3 𝑦𝑒𝑎𝑟𝑠 𝑎𝑡 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑓 10% 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑
annually .Find the compound interest and the amount she has to pay at the end of
3 years.
Through a question let us understand the difference between Simple Interest
and Compound Interest.
Sol: Under Simple Interest Under Compound Interest
1st Year
3rd Year
2nd Year
Interest at 10%
Year-end Amount
Principal
Principal
Interest at 10%
Interest at 10%
Year-end Amount
Year-end Amount
₹ 100.00
₹ 10.00
₹ 110.00
₹ 100.00
₹ 10.00
₹(110+10=₹120.00
₹ 100.00
₹ 10.00
₹(120+10)=₹130.00
₹ 100.00
₹ 10.00
₹ 110.00
₹ 110.00
₹ 11.00
₹ 121.00
₹ 121.00
₹ 12.10
₹ 133.10
Note that in 3 years,
Interest earned by simple
Interest= ₹(130-100)=₹30
Interest earned by Compound
Interest=₹(133.10-100)= ₹33.10
This is the total
simple interest
given for three
years.
This is the total
Compound Interest
given for three years.
14. Q.A sum of₹500 𝑖𝑠 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑 𝑏𝑦 𝑅𝑒𝑒𝑛𝑎 𝑓𝑜𝑟 1 𝑦𝑒𝑎𝑟 𝑎𝑡 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑓 5% 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑
annually .Find the compound interest and the amount she has to pay at the end of
the year.
Q.A sum of ₹750 𝑖𝑠 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑 𝑏𝑦 𝑅𝑒𝑒𝑛𝑎 𝑓𝑜𝑟 2 𝑦𝑒𝑎𝑟𝑠 𝑎𝑡 𝑎𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑓 5% 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑
annually .Find the compound interest and the amount she has to pay at the end of
2 years.
Please do these Questions,as through the method taught
in the previous slides.
15. The method of finding compound Interest, as shown in the previous slides is a bit
complicated, as in such cases we often use formulas.
Suppose P1 is sum on which interest is compounded annually. At a rate of R% per annum.
Let P1 = ₹5000 𝑎𝑛𝑑 𝑅 = 5.
16.
17.
18. Therefore the formula for Compound Interest is~
By using this we only get the amount to be paid at the end of n years, and not
the formula for compound interest.
But as we already know Compound Interest=Total Amount(of n year) – Principal,
so hence we can easily find the Compound interest.
19. Q. Find Compound Interest on ₹12,600 for 2 years at 2% per annum Compounded
Annually.
Solution:
We have 𝐴 = 𝑃 1 +
𝑅
100
𝑛
,where Principal(P) = ₹12,600
Rate(R) = 10,
Number of years(n) = 2
= ₹12,600 1 +
10
100
= ₹12,600
11
10
2
= ₹12,600 ∗
11
10
∗
11
10
= ₹15,246
𝑪𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 = 𝑨 − 𝑷 = ₹ 𝟏𝟓, 𝟐𝟒𝟔 − 𝟏𝟐, 𝟔𝟎𝟎 = ₹𝟐𝟔𝟗𝟔
20. Questions~
Q1.Find the compound interest when Principal = ₹3,000 , Rate = 5% Per annum
and time = 2 years.
Q2.What will be the Compound Interest on ₹4000 in two years when rate of interest
is 5% Per annum?
Q3.Find the principle which will amount to rupees 8788 in 3 years at the
rate of 4% p.a compounded annually
21. Rate Compounded Annually or Half Yearly
(Semi-Annually)
Let us see the difference between Compound Interest compounded annually and C.I.
compounded half-yearly.
23. Some Questions~
Q1. Find the amount and the compound interest on ₹ 8,000 at 10
% per annum for 1
1
2
years if the interest is compounded half-
yearly.
Q2.Find the amount and the compound interest on ₹ 4,000 is 1
1
2
years at 10 % per annum compounded half-yearly.
