Simple and compound interest (1)
- 1. Presentation by: Boivav Hazarika Class :VIII Compound and Simple Interest
- 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’.
- 4. Types of Interest Simple interest Compound 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.
- 9. Calculating Compound Interest (Without using formulae of Compound Interest) Q. 𝐴 𝑠𝑢𝑚 𝑜𝑓 𝑅𝑢𝑝𝑒𝑒𝑠 20,000 𝑖𝑠 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑 𝑏𝑦 𝐻𝑒𝑒𝑛𝑎 𝑓𝑜𝑟 2 𝑦𝑒𝑎𝑟𝑠 𝑎𝑡 𝑎𝑛 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑓 8% 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑 𝑎𝑛𝑢𝑎𝑙𝑙𝑦. Time 2Years Interest 8% Compounded Annually 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑎𝑛𝑑 𝒕𝒉𝒆 𝒂𝒎𝒐𝒖𝒏𝒕 𝑠ℎ𝑒 ℎ𝑎𝑠 𝑡𝑜 𝑝𝑎𝑦 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 2 𝑦𝑒𝑎𝑟𝑠. Steps
- 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.
- 13. The Difference between Simple Interest & Compound Interest
- 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.
- 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.
- 22. Please watch the video
- 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.