SBI PROBATIONARY OFFICERS QUANTITATIVE APTITUDE SIMPLE AND COMPOUND INTEREST

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1 SBI PROBATIONARY OFFICERS QUANTITATIVE APTITUDE SIMPLE AND COMPOUND INTEREST Simple Interest: If the interest is calculated on original Principal for a certain period is called the Simple Interest (S.I.). Simple Interest will be the same for all the years. If P is the principal, R is the rate of interest, T is the time and S.I. is the simple interest, then ( ) PTR TR Simple Interest = Amount = P 1 + Interest is the money that paid for the use of a certain amount. The amount borrowed is called the Principal. The sum of interest and principal is called the Amount. Compound Interest: The compound interest is the interest which is calculated even on the interest. Thus the amount at the end of period becomes the principal for the next period. If A is the amount, C.I. is the compound interest, P is the principal, R is the rate, and T is the time, then ( ) T R A= P 1 + ( ) T R C.I = P 1 + P Note: If the Interest is paid half yearly, time is doubled and the rate is halved. If the Interest is paid quarterly, time becomes 4 times and the rate becomes one fourth. Difference between Simple and Compound Interest Difference between Simple Interest and Compound Interest can be calculated by the following formulae. There is no difference for one year. For 2 years P R Difference = 2 2 For years (00 + R) P R Difference = 2 R

2 EXERCISE 1 1. What principal will amount to Rs.8550 at 4% per annum simple interest in years? 2 1) Rs ) Rs.7500 ) Rs.8 4) Rs.700 5) None of these 2. What is the compound interest accrued on an amount of Rs.18000, at the rate of 5%, at the end of years? 1) Rs ) Rs ) Rs ) Rs ) None of these. A sum of money invested at compound interest will become Rs.650 at the end of first year and 676 at the end of second year. What is the sum? 1) Rs.600 2) Rs.625 ) Rs.700 4) Rs.675 5) None of these 4. What will be the amount on Rs in 2 years at compound interest, if the rates for the successive years be 4% and 5% per year? 1) Rs.26,800 2) Rs.26,725 ) Rs.27,00 4) Rs.27,675 5) None of these 5. A sum of Rs.1400 becomes Rs.1652 in three years at certain rate of simple interest. What will be the amount if the rate of interest is increased by %? 1) Rs.78 2) Rs.1748 ) Rs ) Rs ) None of these 6. A sum was invested at simple interest at a certain rate for two years. It would have fetched Rs.240 more had it been invested at % higher rate. What was the sum? 1) Rs.8,500 2) Rs.4,500 ) Rs.5,600 4) Rs.9,000 5) None of these 7. Population of a town in 2011 was What will be the population in 2014, if it increases annually at 10%? 1) ) ) ) ) None of these 8. The rate of simple interest on a certain amount of money is 6% p.a. for the first two years, 9% p.a. for next five years and 1% p.a. for the period beyond seven years. If the total interest on a sum at the end of ten years is Rs.9120, what is the sum? 1) Rs ) Rs ) Rs ) Rs ) None of these 1 9. What is the compound interest on Rs for 1 year at 8% per annum, interest being calculated 2 half yearly? 1) Rs.225 2) Rs ) Rs ) Rs ) None of these

3 10. A certain sum of money lent out at a certain rate of simple interest per annum doubles itself in 8 years. In how many years will it treble itself? 1) 12 2) 18 ) 24 4) 16 5) None 11. A sum of money will become double in years at compound interest. In what time will it become four times itself? 1) 9 yrs 2) 6 yrs ) 12 yrs 4) Can't be determined 5) None 12. A certain sum of money becomes Rs.1250 in a span of 5 years and further to Rs.1700 in the span of 8 years at the same rate of simple interest. What would be the amount at the end of 12 years? 1) Rs.225 2) Rs.2500 ) Rs ) Rs ) None of these 1. What is the difference between simple and compound interest for three years on Rs at 8% p.a? 1) Rs.48 2) Rs.122 ) Rs.496 4) Can't be determined 5) None 14. A sum of money amounts to Rs.1488 in years at a simple interest. If the rate of interest is raised by 25%, the sum amounts to 1560 during the same period. Find the sum. 1) Rs.150 2) Rs.1500 ) Rs ) Rs ) None of these 15. A sum of Rs.7200 is lent out in two parts in such a way that the interest on one part at 8% p.a for years is same as on the other part at 5% p.a. for 6 years. Find the first part. 1) Rs.200 2) Rs.600 ) Rs.00 4) Rs ) None of these KEY 1-2; 2-; -2; 4-; 5-4; 6-5; 7-1; 8-1; 9-; 10-4; 11-2; 12-5; 1-5; 14-; ( ) TR 1. Amount = P P ( 1 + ) = P = = Rs EXPLANATIONS 1 1 For one year, rate of interest is 4% and for years it is 4 = 14% 2 2

4 The amount will become 114%. If 114% money = 8550, then % money ( ) R T 2. C.I = P P = 8550 = Rs C.I = ( 1 + ) [ ] = Amount = 105% of 105% of 105% of = C.I = = Rs Interest on Rs.650 is = Rs Rate of interest = = 4% 650 R T Amount = P ( 1 + ) = P ( 1 + ) P = = Rs.625 ( Amount is ) ( 1 + ) A = = Rs.2700 SI R = R = = 6% P T 1400 Now the rate of interest is 6 + = 9% ( TR New amount is P 1 + ) ( 9 = ) = Rs.1778 If the rate of interest is increase by % then the amount will also increase by that much 1400 New interest is = Rs.126

5 New amount is = Rs It fetches Rs. 240 more in 2 years. It fetches Rs.120 more in one year. that means % = Rs.120 % (sum) is 120 = Rs Population after years ( ) is 110% of 110% of 110% of = Let the principal be Rs.x x 2 6 x 5 9 x = 9120 x ( ) = 9120 x = Rs As interest is calculated half yearly, 1 1 will be half years and the rate percent will be 4% per half 2 year. now, R = 4% and T = 4 C.I. = ( 1 + ) = Rs Let the principal be Rs.P and the amount will be Rs.2 P (2P P) Rate of interest per annum is = 12.5% P 8 (P P) Required time is = 16 years P 12.5 Amount doubles in 8 years means to get % interest it takes 8 years To become treble means to get 200% interest it takes = 16 years 11. Let the money be Rs. It becomes Rs.200 in years Again Rs.200 will become Rs.400 in another years (... Compound interest) amount will become four times in + = 6 years 12. Interest for years (8 5 years) = = Rs Interest for 5 years = 450 = Rs.750 Principal = = Rs.500

6 12 Interest for 12 years = 450 = Rs.1800 Amount after 12 years = = Rs.200 (00 + R)P R 2 1. Difference for years is = Rs Rs.1560 Rs.1488 = % of interest = Rs.72 % interest = 72 = Rs The interest for three years = Rs.288. Therefore Principal = = Rs Let the first part be Rs.x, then the second part will be (7200 x) x 8 (7200 x) 5 6 = x = Rs.4000 Writer: Dr. G.S. Giridhar

The Institute of Chartered Accountants of India

The Institute of Chartered Accountants of India CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY- APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able