SI, CI and Installments
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1) The document discusses the key differences between simple interest (SI) and compound interest (CI). With SI, interest is calculated on the principal only, while with CI interest is calculated on the principal and previously accumulated interest. 2) Several examples are provided to illustrate how the amount grows faster with CI compared to SI over multiple time periods. The formulas for calculating SI, CI, and interest compounded n times per year are also outlined. 3) The document concludes by providing several word problems to practice calculating SI, CI, and loan installments in different scenarios.
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$31
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SI, CI and Installments
- 1. CAT Simple Interest Compound Interest and Installments 1
- 2. Basic terms involved Principal (P) Interest (I) Rate of Interest (r) ---- usually expressed in per annum Time(n) ------------------usually expressed in years, otherwise converted to years to match r’s units. Amount(A)
- 3. Difference between SI and CI explained Year Simple Interest Compound Interest P I A P I A 1st 2nd 3rd P = Rs. 1000 r = 10% per annum Year Simple Interest Compound Interest P I A P I A 1st 1000 100 1100 1000 100 1100 2nd 1000 100 1200 1100 110 1210 3rd 1000 100 1300 1210 121 1331 3
- 4. Difference between SI and CI for 2 years P = Rs. 1000 r = 10% per annum Year Simple Interest Compound Interest P I A P I A 1st 1000 100 1100 1000 100 1100 2nd 1000 100 1200 1100 110 1210 3rd 1000 100 1300 1210 121 1331 4 Year Simple Interest Compound Interest P I A P I A 1st 100 100 2nd 100 110 3rd 100 121 For 2 years = P (r/100)2 (also for second year) For 3 years = P (r/100)2 (r/100 +3)
- 5. Observations from the CI table P = Rs. 1000 r = 10% per annum Year Compound Interest I A P I A 1st 100 1100 1000 100 1100 2nd 110 1210 1100 110 1210 3rd 121 1331 1210 121 1331 r r R when two amounts/interests are given 5
- 6. SIMPLE Interest COMPOUND Interest Interest Amount Simple Interest and Compound Interest Formulas 6 SIMPLE Interest COMPOUND Interest Interest Pnr/100 A-P Amount P + SI P(1+r/100)n
- 7. Compounding n times a year – nominal and effective rate of interest Half yearly Quarterly Monthly 15 times a year Compounded every moment 7
- 8. Problems Rs 1000 is being charged @50% per annum. What is the interest for 3rd year at compound interest? 1. 1125 2. 2375 3. 1150 4. None of these Answer: Option 1 8
- 9. Problems Rs. 10000 is being compounded @ 20 % per annum. If the interest is compounded half- yearly. What will be the amount after 2 years? 1. 14641 2. 13310 3. 12100 4. None of these Answer: Option 1 9
- 10. Problems After two years SI and CI on a sum are Rs. 400 and Rs. 440 respectively. What is the principal? 1. 1000 2. 500 3. 2000 4. None of these Answer: Option 1 10
- 11. Problems A sum of money doubles in 10 years. How many years it will take to become 4 times of itself at the same rate of simple interest? 1. 20 2. 15 3. 30 4. None of these Answer: Option 3 11
- 12. Problems A sum of money doubles in three years when compounded annually and it becomes x % of itself in 12 years. What is the value of x? 1. 12 2. 1600 3. 600 4. None of these Answer: Option 2 12
- 13. Problems Out of a sum of Rs. 750, a part was lent @5% SI and the other @10% SI. If the interest on the first part after 2 years and interest on the second part after 4 years are equal. What is the value of the second part? 1. 120 2. 100 3. 150 4. None of these Answer: Option 3 13
- 15. Problems – Installment on SI Ashok purchased a shirt costing Rs.2400 and paid Rs. 1000 as down payment and two monthly installments of Rs. 800 each paid at the end of each month. What is the rate of interest? 1. 100 2. 20 3. 120 4. None of these Answer: Option 3 15
- 17. Problems – Installment on SI A man borrows Rs. 8160 from a bank and has to return in two equal annual installments paid at the end of the first and second year respectively. If the rate of interest charged is 12.5% p.a. compounded annually, find the annual installment. 1. 5220 2. 4480 3. 4860 4. 4590 Answer: Option 3 17
- 18. Problems – Installment on SI A man borrows Rs. 63000 from a bank and has to return in two equal annual installments paid at the end of the first and second year respectively. If the rate of interest charged is 10% p.a. compounded annually, find the annual installment 1. 35000 2. 36300 3. 48600 4. 38700 Answer: Option 2 18