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Annuities and interest in business mathematics

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Annuities and interest in business mathematics

1. 1. ANNUITIES AND INTEREST IN BUSINESS MATHEMATICS <ul><ul><li>by : </li></ul></ul><ul><ul><li>DR. T.K. JAIN </li></ul></ul><ul><ul><li>AFTERSCHO ☺ OL </li></ul></ul><ul><ul><li>centre for social entrepreneurship </li></ul></ul><ul><ul><li>sivakamu veterinary hospital road </li></ul></ul><ul><ul><li>bikaner 334001 rajasthan, india </li></ul></ul><ul><ul><li>FOR – CSE & PGPSE STUDENTS </li></ul></ul><ul><ul><li>(CSE & PGPSE are free online programmes </li></ul></ul><ul><ul><li>open for all, free for all) </li></ul></ul><ul><ul><li>mobile : 91+9414430763 </li></ul></ul>
2. 2. My word..... <ul><ul><li>My purpose here is to give an introductory lesson on annuities and interest. It will help you in your analytical skills. Let us change the society, change the world. Go with positive spirit. Please pass this presentation to all those who might need it. Let us spread knowledge as widely as possible. I welcome your suggestions. I also request you to help me in spreading social entrepreneurship across the globe – for which I need support of you people – not of any VIP. With your help, I can spread the ideas – for which we stand.... </li></ul></ul>
3. 3. 9% compounded quarterly is equal to The semi-annual effective rate is: A) 9.10%. B) 9.31%. C) 9.20%.
4. 4. solution... Suppose you pay interest @ 9 % compounded quarterly, it means you are paying 9/4% every quarter and interest is added in the principal every time. Suppose you start with 100. After 1 st quarter, 100 will become : (100+2.25) = 102.25 after 2 nd quarter = (102.25 *1.0225) = 104.55 thus on semi-annual basis we are getting interest of 4.55 or 9.1% p.a. Semi annually compounding Answer
5. 5. What is the annual effective rate, if there is continous compounding rate of 9% ? Formula of rate = e^(rate) - 1 =(2.71828)^(.09) -1 = rate is 9.417% answer
6. 6. I invest Rs. 1000 every year from today onwards for 10 years. Rate of interest is 8%. Calculate future value of annuity ? Formula = amt (((1+rate)^n – 1) / rate ) =1000(((1.08^10)-1)/.08) =14486.56 but here I am starting my investment from today, so this first instalment, the interest will also be added : 14486.56 * 1.08 =15645.48 answer
7. 7. What is log? Here we use shortcuts to exponentials for speedy calculations. logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce that number. For example, the logarithm of 1000 to base 10 is 3 it can be written as : log 10 1000 = 3 usually we use the base of 10, so we can write : log 1000 = 3
8. 8. What is log 10 100000? = 5 answer
9. 9. What is natural log ? Here the base is e, which is 2.71828 (not 10, which we had discussed earlier).
10. 10. What is log 2 8? = 3 (here base is 2, and we know that 2^3 = 8)
11. 11. What is log 1982 1? Answer = 0 We know that in any base b, the logarithm of 1 is 0.
12. 12. What is log b b^x = ? Answer = x it is a rule that : log b b^x = x
13. 13. What is : 5 = log 2 n ( what is n?) 32 (answer ) 2^5 = 32
14. 14. What is log 10 .001 = -3
15. 15. Find log of 1728 to the base 2*sqrt(3) ? Let us take factors of 1728 : 2*2*2*2*2*2*3*3*3 thus we know that 2*sqrt(3) ^ 6 = 1728 so answer is 6.
16. 16. Change the base of log 200 to 2? = log 2 200 / log 2 10
17. 17. Given: log 2 = .3010 log 3 = .4771 log 5 = .6990, what is log 6? We know that log 6 = log 2 * 3 we know that log 2*3 = .3010+.4771 =.7781
18. 18. Given: log 2 = .3010, log 3 = .4771 Evaluate log 18. Log 2 * log 3*log 3 =.3010+.4771+.4771 =1.2552
19. 19. Given: log 6 = .7781 Use the laws of logarithms to evaluate log 600 =log 6 * 100 = .7781 + 2 = 2.7781 answer