 ताज्न आप पूर आप आद उनने बिस्छक्टन काँ आपुरी नहींगउड़़्ो। हो जब आप तिक्ररश्ट कोट कोडा इक्टा इत्र अईँन बाटने अद़् है है। एक बग फुँट एहमियत के हामिलोतें रहा? आन वोप एहमियत के हामिलोगाले चन्द फक्तस में अंप्रश रहे एक पक्तर के धिर कहते हैं। तिस को आब बभब ऊquant factor कना जाते है ठौत एक लुद बत्तर हैं। अब आप ये ख़्द श्वरेटते शब Ramya, it is important to know what is interest rate, and how can we calculate it, the changes in it, how can we influence our financial decisions. So first of all, I'll define the interest rate, that is charge, that is money, that you pay, that you borrow the principle amount, अब नप कुछ प्यषा बवारो की आप उसके उपर अभ ज़्वाव यब आप प्रन्स्यपल मांए हो गो भि आवाव बारो की है उस को थो आप चारज विखाना का, जारज लिए देते हो, उस को हम णिए अप थ्पीऊट से विश्टेन करते हैं. ये ट्स चारबूर्व मुनि इस वो स्था तो एक सब आईजागे रूए। डूई मिक लिसकतान और मँई और लोगे से लिये वो था लिझा बिसवोले के लग मुनि आईगार नहीं अपरेट कर सकतें असकिलिए आपको उसकी कोस पीर करने परतीग है और वो खोस तो आपका लोगे लागे लागी लेती है और आबी इंट्र्स रेत को किस खिष खिष्ट दिखवेशच्यान फिर में हम आपको कलटेट कर सकते हैं और सब जाजक टेजजेश के में कितना इमए तो उसको ज़ुग डिसकूष करने के लिये अबि मैं आप के साथ डिसकास करने वाली हुं एक आप ट्याज़े ख़ेट एक अप व्ट्याज़ुमाद तो weam sabse pehle discuss karenge simple loans pehre ہम discuss karenge fixed payment loan और pehre हमारे पास है कुड्ँटक बो रन्गा और us kepohaad haam discuss karenge Discount आस दिया 0 ख्यो कुपाऊन भंगा तो abhi sabse pehle simple loan क्या होती एक? तो simple loan में क्या है के आप एक सर्टन ताएं पिरियsters के लीए न мाने बारो ?] अगर आप स्थन फिक्स्ट रेट अप इंट्रूस्त आप को बताया जाते है पेंग या जो भी फिनिन्ट्चल किया निस्चूँन से या निदबिज्ट मुनि आप यहां भैसी पैसे पचाूँ किया अपको बतायागी के आपको एक साल में इतना एकस्फरा मनी हमें इंट्रुस्त के तोर पे इस प्रन्च्पल आमाच्ट के उपर पेख़ना पडेगा जितना दूरेशन आप आप आपने पास उस मनी को रखते हो उसके इसाप से आपकी जो मनी ये वो जो आपने रीपे करनी आप आद पोती जाती है तो एक चोता सा एकजमपल यहा आप को ते पुस, एक दॉलर पे एक साल के गुजर जाने के बात, मिले देने पड़िंगे, एक डॉलर अर दुस्पेन्स. और तो साल तक अगर में वो एक डॉलर अपने पास रे्तेन करने वाली हूं, जिस पे मुझे आपताय गया अगे, after 2 years, I will have to repay 1.21$ similarly, after 3 years, it will be 1.33$ and if I want to write a formula that if I tell a certain number of years, it is n and how much amount I have to repay after going through n number of years then we calculate it very easily if I want to multiply 1$ 1 plus your interest rate is 10% I have assumed in the example your interest rate will be 10% you will write it in the place of I and 1 plus I raise to the power n n will tell you the number of years whatever time period you have to see how much money I have to repay or how much money someone else has to repay in the context of simple interest then you can calculate it but if we know that in the future whoever has borrowed 100$ from me and after 5 years, he will repay 100$ after 5 years, whoever has returned 100$ the things I can buy from him the things I can buy from him cannot be equal this means that 5 years down the lane the 100 rupees I will get the purchasing power of that money must have gone down it will not be equal to 100$ to estimate this if I give 100$ to a person and the interest rate for example 8% or 10% for 5 years if someone has told me lend me the money give me the loan so how much money should I ask for after 5 years which is equal to 100$ so for that context we use the concept of present value and present value as I told you what I did to get the future value my principle was 1$ I multiplied it with 1 plus I raise to the power n so to get the present value you multiply it with 1 plus I raise to the power n because you have to make less money so you will divide it so you will keep it in the numerator 1$ and you will keep it in the denominator 1 plus I raise to the power n so n will tell you after how many years you are dealing with what is your time duration that will specify the time in number of years and if for example 1.5 years or 6 months or 0.5 years or 1.5 years that is something which needs to be accounted for and the I you have to keep that is the interest rate which you are lending on the Sharai Sood so from this formula you can calculate your present value by dividing the principal amount with 1 plus I raise to the power n so this will give you present value next the thing in the whole context we have to understand that is the interest rate we are talking about yield to maturity what is the meaning of yield to maturity that if a person has told me or the company has told me that you give us 1.000.000 and after 2 years we will give you 2.000.000 so I have to account for what is the interest rate on the interest rate this money is getting back so what is the interest rate on which we can say yield to maturity after 2 years what is the benefit of yield so the interest rate can also be considered in the context of our financial economics we take the interest rate yield to maturity and for yield to maturity I have discussed two types of formula for future value if you know that somebody has offered me that you give me 1.000.000 and after 2 years we will give you 2.000.000 so how will I know what is the yield to maturity so for that the formula which we use is the difference between these two amounts that is 2.000.000 minus 1.000.000 in numerator and in denominator I have to write 1 plus i and to solve this for i this particular expression which we have discussed for present value for example I will solve this particular expression for i so I will be able to come up with the value of yield to maturity or what I have written here I will try to explain it with the help of it that if somebody has offered me after a year after taking 1.000.000 then I will return 110.000 after a year so my n is 1 so I have not written here so n is 1 and what is the yield to maturity so what I have done I will use this formula that future value is 110 divided by 1 plus i is equal to the present value of 100.000 100.000 I will solve this particular expression for i so I will get the value for yield to maturity in this context because after a year I am getting 110.000 present value of that money which I have taken at the beginning that is 100.000 so in this expression I have written as 10% so you feel if we give 100.000 and after a year it will become 110.000 so yield to maturity in this case will be 10% so in this way you can calculate yield to maturity or interest rate next important concept I have told you that we can do lending and borrowing this is a simple loan as I have given you examples then there could be fixed payment loan fixed payment loan means that you have lent some money to a company and that company says that in the next 10 years or next 15 years or next 20 years you will be given a fixed amount of money this amount which you have lent to return it so in this context what you have to do you have to calculate yield to maturity you do not have a value your repayment is fixed and that is going on over a period of time so period of time can be 10 years it can be 15 years it can be 20 years as you take a car you lease from a bank you took a car you took some down payment and now you are making a certain walk and every month after every 3 months after every 6 months after equal intervals of time you repay that kiss so you have to repay till 5 years every month this is 30,000 to 35,000 rupees you have borrowed a car or you have leased and similarly when you lease the house even then you have to repay the fixed amount so these are the two examples in our fixed payment loan to explain the concept you can use and in fixed payment loan how will you take out yield to maturity I have written a formula for that our old formula but since there is no repayment there are multiple points so on the right hand side of your equation you will have to apply multiple points for example if somebody has said that you give me 1000 dollars and after every 1 year after 1 year I will return 126 dollars and this return will last for 25 years so if I have to imagine that in transaction in this loan day my yield to maturity so what I have to do I have to write 1000 on the left hand side and every year I have to divide the repayment from 1 plus i raised to the power n so for the first year I will divide the money from 1 plus i raised to the power 1 and for the second year I will divide the payment from 126 divided by 1 plus i raised to the power 2 and in the same way the repayment of 25 years of 126 dollars I will divide it from 1 plus i raised to the power 25 and I will collect all these terms after collecting I will solve it for i i will tell yield to maturity or my interest rate on which this particular transaction is being calculated now you must be thinking about how it will be for that we have financial operations calculators so by using that calculator we have stream cash inflows cash outflow over a period of time we can calculate it with the help of those calculators if you get excel you can use this particular concept to calculate the value of yield to maturity or interest rate next generally this is an example if we want to develop a general formula and in that perspective in fixed payment loan how to yield to maturity or any of your unknown formula you can remove it or if we have to either yield to maturity or interest rate to charge and one person wants to borrow 5 lakh rupees or company wants to borrow 5 lakh rupees so the fixed payment on an annual basis or after 6 months how much should be the cost 12% so for that this is the formula that is lv is the loan value fp is the fixed payment which you will expect to calculate if you are not given if you are given i or lv loan value then you can remove fp if you know fp the fixed yearly cash flow you know the payment of cash and the loan value you can calculate yield to maturity or interest rate so there are 3 unknowns you will know the value of 2 you can calculate the value of 3 with the help of this equation so what we did we said suppose somebody a company asked me to lend them 500,000 rupees and interest of for example 12% so every year from them how much money i should take 12% interest charge so in this equation i will pay 12% lv will pay 5,000,000 and this particular expression i will solve for fp so i will be able to find out what is the value of my fixed payment and as much as you have terms on the right hand side this will be one term for every year if you are not paying it it can be monthly payment there are 4 payments 6 payments, 20 payments you have to add these terms on the right hand side to account for the amount of payments our payments are so this is how you can find out the loan value you can find out the fixed yearly payment which you should get if you know the yield to maturity and if you know the fixed payment you know the loan value and you want to find out the yield to maturity again the same formula can help you in finding out that value as well