Compound interest and related problems in business mathematics

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Compound interest and related problems in business mathematics

  1. 1. COMPOUND INTEREST AND RELATED PROBLEMS 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. A sum of money placed at C.I doubles itself in 5yrs .It will amount to 8 times itself in how many years? 1 to 2 in 5 years 2 to 4 in 10 years 4 to 8 in 15 years answer = 15 years
  4. 4. If the S.I on sum of money at 15% per annum for 3yrs is Rs.1200, the C.I on the same sum for the same period at same rate is? Interest for 1 year = 1200/3 = 400 principal = 100/15 *(400) =2666.67 compound interest = formula : = principal (1+rate) ^n n =number of years =2666.67(1+15/100)^3 =4055.67 answer
  5. 5. The difference between C.I and S.I on a sum of money for 2 yrs at 10% per annum is Rs.150.the sum is Let us assume that principal = 100 SI on 100 = 20 (10 per annum) CI on 100 = 100 *( (1+10/100)^2-1) CI = 21 difference between 21 and 20 = 1 if 1 is the difference, principal = 100 so if difference is 150, principal should be : 150/1 * 100 = 15000 answer
  6. 6. The amount of Rs.7500 at C.I at 4% per annum for 2yrs is Formula : = principal (1+rate)^n where n = number of years =7500*(1+4/100)^2 =8112 answer
  7. 7. .A sum of money amounts to Rs.6690 after 3 yrs and to Rs.10035 after 6 yrs on C.I .find the sum Amount increase from 3 to 6 years (gap of 3 years), if we want the original amount, we have to reduce it in same proportion from 3 to start (gap of 3 years). In order to reduce, put the smaller amount as numerator and bigger amount as denominator. Reduce the amount in the same proportion : 6690 * 6690 / 10035 =4460 answer
  8. 8. If C.I on a certain sum for 2 yrs at 12% per annum is Rs.1590. What would be S.I? SI = simple interest CI = compound interest We can calculate SI here without calculation of principal amount. We know that if 100 is deposited, @12%, SI will be 24. if this amount is deposited at CI, the interest will be : 12 + .12*(112) 13.44 total interest as CI = 25.44 thus SI = 24/25.44 * 1590 = 1500 answer
  9. 9. A certain sum amounts to Rs.7350 in 2 yrs and to Rs.8575 in 3 yrs.Find the sum and rate%? 8575 – 7350 = 1225 rate = 1225/7350 * 100 rate =16.66% formula = amount (with interest) / (1+rate)^n principal = 7375 /((1+16.66/100)^2) =5419 answer
  10. 10. If the difference between C.I compounded halfyearly and S.I on a sum at 10% per annum for one yr is Rs.25 the sum is? Let us assume that principal is 100 interest on SI = 10 interest on CI = 100*((1+10/200)^2) =110.25 the diference is .25 if the difference is .25, principal is 100, if the difference is 25, principal = 10000 answer
  11. 11. A man borrowed Rs.800 at 10 % per annum S.I and immediately lent the whole sum at 10% per annum C.I What does he gain at the end of 2yrs? SI on 800 = 160 (for 2 years) CI for 2 years formula : principal * ((1+rate)^n – 1) =800*(((1+10/100)^2) -1) =168 his gain = 168-160 = 8 answer
  12. 12. On what sum of money will be S.I for 3 yrs at 8% per annum be half of C.I on Rs.400 for 2 yrs at 10% per annum? formula : principal * ((1+rate)^n – 1) CI = 400 *(((1+10/100)^2)-1) =84 half of 84 = 42 42 is for 3 years, so for 1 year : 14 principal = (100/8)*14 = 175 answer
  13. 13. 9% compounded quarterly is equal to The semi-annual effective rate is: A) 9.10%. B) 9.31%. C) 9.20%.
  14. 14. 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
  15. 15. 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
  16. 16. 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
  17. 17. What is future value ? Future value takes up interest and therefore it is more than the sum invested. If I invest 1000 today, with an interest rate of 10%, it will become 1100 after 1 year.
  18. 18. Formula for present value ? Amount / (1+rate) ^ number of years suppose 1221 is due after 3 years and rate of interest is 10%, present value is : 1221 / (1+10/100)^3 =917.35 answer
  19. 19. What is the formula for future value ? Amount *(1+rate) ^ number of years suppose 1000 is invested for 3 years and rate of interest is 10% annually compounding, future value is : 1000 * (1+10/100)^3 =1331 answer
  20. 20. How to calculate EMI? You may use the formula for present value of annuity. Here you need a factor formula = ((1+rate)^n -1) / (rate(1+rate)^n) here n= number of instalments rate = rate % / number of instalments in a year*100 EMI = amout to pay / factor of annuity(calculated from above formula)
  21. 21. What will be EMI for Rs. 5 lakh rate of interest = 10%, payable in 20 annual instalments = ((1+rate)^n -1) / (rate(1+rate)^n) ((1+10/100)^20 - 1)/(10/100 (1+10/100)^20) =5.73/.67 =8.55 EMI=500000/8.55 =58479 ANSWER
  22. 22. What will be EMI for Rs. 5 lakh rate of interest = 10%, payable in Monthly instalments in 20 years. = ((1+rate)^n -1) / (rate(1+rate)^n) ((1+10/1200)^240 - 1)/(10/1200* (1+10/1200)^240) 6.328 / .061 =103.624 EMI = 500000 / 103.624 =4825 ANSWER
  23. 23. What is sinking fund ? If you deposit a sum of money every year and you are able to have a lot of money after some time this is sinking fund you create sinking fund to purchase a new machinary / building etc it is just reverse of the EMI (where you were looking at present value of annuities), because here you are taking future value of annuities.
  24. 24. How to calculate sinking fund contribution? For calculation of sinking fund contribution, we have to use the following formula : = ((1+rate)^n -1 )/(rate) here n = number of instalment rate = rate / number of instalments in a year*100.
  25. 25. Jigyasa has to collect 1 ml. After 5 years to start a new factory. How should she save every month? Rate = 12% = ((1+rate)^n -1 )/(rate) =((1+12/1200)^60 -1) / (12/1200) =.8167 / .01 dividing factor =81.669 monthly savings = 1000000/81.669 =12244.44 per month answer
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