CHAPTER 4 SIMPLE & COMPOUND INTEREST INTEREST Basic terms associatted with this topic: Interest : It is the time value of money. It is the cost of using capital. Principal : It is the borrowed amount. Amount : It is the sum total of Interest and Principal. Rate : It is the rate percent payable on the amount borrowed. Period : It is the time for which the principal is borrowed. Interest can be classified as: Simple Interest : Simple Interest is payable on principal. Compound Interest : Compound Interest is payable on Amount. Basic formulas related to Simple Interest Simple Interest (SI) = PRT Here P = principal, R = rate per annum, T = time in years PRT RT Amount (A) = P P1 or P + SI If time is given in month, & Rate is given per annum, PRT then SI 1 If time is given in weeks, & Rate is given per annum, PRT then SI 65 Also, SI Rate PT SI Time P R SI Principal T R If amount is given then, Amt Principal (R T) 1 : Find the simple interest and amount when ` 0 is lent at 5% per annum for 5 years. Sol. By the formula, SI = PRT 0 = ` 60 Amount = P + SI = + 60 = ` 1060 : Find the principal when simple intrest is ` 60 at 4% per anum for 4 years. Sol. Principal = SI 60 = ` 750 RT 4 : In how many years will the sum of `500 become ` 60 if the rate of simple interest is 4% per annum? Sol. Using the formula, SI T R P Here, SI = 60 500 = ` 10 10 T = 6 years 500 4 4 : At what rate percent per annum will a sum of money double in 8 years? Sol. Let principal = ` P Then SI = ` P and Time = 8 years Rate = = SI P T P P 8 8 = 5 1 1 % per annum Basic formulas related to Compound Interest If interest is compounded annually, R Amt P1 N
D-5 NUMERICAL ABILITY 5 If interest is compounded half yearly, 8 8 8 N = 5100 R 80 80 80 Amt P1 00 = `57178.70 C.I. = `(57178.70 5100) If interest is componded quarterly, = `5978.70 4N R Amt P1 400 If the rate of interest changes over the years, then R1 R Amt P 1 1... Compound Interest for all the above cases = Amt Principal. Difference between C.I & R SI for two years P PR (00 R) Difference between CI & SI for three years () 5 : Find the compound interest on ` 000 at 5% per annum for years, compound annually. Time Rate Sol. Compound interest = Principal 1 1 5 = 000 1 1 1 = 000 1 0 = 961 8000 000 8000 = 000 161 8000 = `15.5 6 : Find the compound interest on ` 5000 for years at 6 % per annum compounded half yearly. R Sol. Using the formula, A P1 00 T 6 = 5000 1 00 = 5000 (1.0) 6 = 5971 (to nearest rupee) Compound interest = 5971-5000 = ` 971 7 : Find the compound interest on ` 5100 for 9 months at 15 % per annum compounded quarterly. Sol. Here, Time = 9 months = quarters Now, using the formula 8 : Find the compound interest on ` 5000 for years at 6 % per annum for first year, 7% for the second year and 8% for the third year Sol. Using the formula, R1 R R = P1 1 1 6 7 8 1 1 1 = `615 C.I. = 615 5000 = `115 9 : The compound interest on `000 in years is ` 696.0 and simple interest on the same amount is ` 660. What is rate of interest per annum? Sol. Difference of interest = P R R 696.0 660 = 000 1.1 R 0 00 R = 11 R = 11% 10 : The difference between compound interest and simple interest on a certain sum of money in years at the rate of 7% per annum is ` 5.645. What is the principal? R (00 R) Sol. Difference of interest = P () (7) (00 7) 5.645 = P () 5.645 P = 4907 = ` 15000 11 : A person has taken a loan amount at the rate of 10 % annual compound interest and he pays that amount in two instalments of ` 968 each. How much loan did he take? Sol. Loan taken = 968 968 1 10 10 1 1 4T R 15 A P1 5100 1 400 400 15 = 5100 400 400 = 415 5100 400 1 1 968 11 11 10 10 10 10 968 11 11
Simple & compound interest 5 D-5 10 1110 10 968 11 = 10(11 10) 968 1111 10 1 968 = `1680 11 11 1 : A sum of money doubles itself in 5 years. Find the simple rate of interest. Sol. Let the sum of money, i.e. P = It doubles itself, i.e. Amt = 00 SI = Amt Principal = 00 = Time = 5 years SI Rate PT 0% 5 Alternately In these types of questions, (No.of time 1) Rate Time ( 1) Time 0% 5 The same formula can even be applied for tinding time in the above pattern of questions. 1 : Mohan borrows `10,000@ 8% pa for 4 years. At the end of the period, he pays ` 6000 in cash, and for the balance amount, he gave his mobile. Find the cost of the mobile. P R T 10, 00084 Sol. SI 00 Amount = P + SI = 10,000 + 00 = 1,00 Cost of Mobile = 1,00 6000 = 700 14: Mohan borrows `10,000 from two money lenders at a rate of 6% pa and 8% pa respectively, for a period of years. If the total interest he paid was ` 1980, find the amount borrowed at the rate of 6% pa. Sol. Let the amount borrowed at 6% pa be x. and the amount borrowed at 8% be y So, x + y = 10,000...(i) Now, x6 18x SI, and y8 4y Also SI According to the condition, 18x 4y 1980 or 18x + 4y = 198000...(ii) On equating (i) and (ii), we get x = 7000 and y = 000. Therefore, amount borrowed @ 6% pa = 7000.
D-54 NUMERICAL ABILITY 54 SOLVED EXAMPLES 1: What would be the simple interest obtained on an amount of ` 6,55 at the rate of 10% p.a. after 6 years? (a) ` 414 (b) ` 91 (c) ` 807 (d) ` 149 (e) Sol. (b) None of these PRT Simple interest = ` 91 : What would be the compound interest obtained on an amount of ` 7800 at the rate of 5% p.a. after years? (a) ` 15.685 (b) ` 19.475 (c) ` 187.68 (d) ` 148.750 (e) Sol. (b) None of these 5 Compound interest 7800 1 1 105 7800 1 105105105 7800 = (7800 0.15765) = `19.475 : If the difference between the simple and the compound interest earned on a sum of money at the rate of 5% p.a. for years is ` 16, find the principal. (e) Sol. (b) EXERCISE (a) `6,00 (b) `6,400 (c) `6,50 (d) Cannot be determined None of these If the difference between CI and SI for two years is given, then Difference () Principal (Rate) 16 = `6400 55 4: The simple interest accrued on an amount of ` 19,800 at the end of three years is ` 7,18. What would be the compound interest accrued on the same amount at the same rate in the same period? (a) ` 894.6784 (b) ` 8017.5744 (c) ` 7861.8754 (d) Cannot be determined (e) Sol. (b) None of these Interest 718 Rate 1%p.a. Principal Time 19800 Time Rate C.I. Principal 1 1 1 198001 1 19800 [(1.1) 1] = ` 8017.5744 1. Anil invested an amount for three year at a simple interest rate of 9% p.a. He got an amount of ` 19,050 at the end of three years. What principal amount did he invest? (a) `14,500 (b) `11,050 (c) `1,440 (d) `10,950. What will be the compound interest on an amount of ` 5,000 for a period of year at 8% p.a? (a) ` 840 (b) ` 400 (c) ` 8 (d) ` 416. What is the interest received on a principal of ` 450 for yea if the interest received on ` 1 after four year at the same rate of simple interest is ` 0.40? (a) ` 90 (b) ` 180 (c) ` 6 (d) Cannot be determined 4. Ms. Sandhya deposits an amount of ` 1,400 to obtain a simple interest at the rate of 1 per cent per annum for 8 years. What total amount will Ms. Sandhya get at the end of 8 years? (a) ` 1,444 (b) ` 61,544 (c) ` 41,544 (d) ` 1,144 5. What amount of compound interest can be obtained on the
Simple & compound interest 55 D-55 principal amount of ` 15800 at the rate of 6 per cent per annum at the end of year? (a) ` 1,986 (b) `,01.48 (c) ` 1,95.88 (d) ` 1,956 6. Mr. Deepak invested an amount of ` 1,50 for 6 years. At what rate of simple interest will he obtain the total amount of ` 6,50 at the end of 6 years? (a) 6 % p.a (b) 5 % p.a (c) 8 % p.a (d) 1 % p.a 7. What approximate amount of compound interest can be obtained on an amount of `,080 at the rate of 7% p.a. at the end of year? (a) ` 586 (b) ` 69 (c) ` 646 (d) ` 596 (e) ` 61 8. Arunima invests an amount of ` 10,50@4% p.a. to obtain a total amount of ` 1,710 on simple interest after a certain period. For how many year did she invest the amount to obtain the total sum? (a) 6 years (b) 8 years (c) 5years (d) 4 years 9. Sudhanshu invested ` 15,000 at interest @ 10% p.a for one year. If the interest is compounded every six months what amount will Sudhanshu get at the end of the year? (a) ` 16,57.50 (b) ` 16,5000 (c) ` 16,55.50 (d) ` 18,150 10. What should be the simple interest obtained on an amount of ` 5,760 at the rate of 6% p.a. after years? (a) ` 106.80 (b) ` 1666.80 (c) ` 16.80 (d) ` 106.80 11. Ms Suchi deposits an amount of ` 4,000 to obtain a simple interest at the rate of 14% p.a. for 8 years. What total amount will Ms Suchi get at the end of 8 years? (a) `5080 (b) `8000 (c) `50880 (d) `6880 1. Asmita invests an amount of ` 955 at the rate of 4 per cent per annum to obtain a total amount of ` 1144 on simple interest after a certain period. For how many year did she invest the amount to obtain the total sum? (a) 10 years (b) years (c) 5 years (d) 4 years 1. Ms. Neelam deposits an amount of ` 1640 at simple interest and obtained ` 5451 at the end of 5 years. What was the rate of interest per year? (a) 10.5% (b) 1% (c) 1.5% (d) 11% 14. Girish invested a certain amount at the rate of 8% p.a. for 6 year to obtain an amount of ` 8,046. How much amount did Girish obtain as simple interest? (a) `1,550 (b) `9,096 (c) `18,950 (d) Cannot be determined 15. Ms. Maya deposits an amount of ` 17,800 and obtained ` 1,684 at the end of 6 years. What was the rate of simple interest per year? (a) 14.5 (b) 11 (c) 1.5 (d) 1 16- The simple interest accrued on an amount of ` 84,000 at the end of three year is ` 0,40. What would be the compound interest accrued on the same amount at the same rate in the same period? (a) ` 0]01-95 (b) ` 1]01-95 (c) ` ]01-95 (d) ` ]01-95 (e) ` 4]01-95 17. Veena obtained an amount of ` 8, 76/- as simple interest on a certain amount at 8% p.a. after 6 years. What is the amount invested by Veena? (a) ` 17,180 (b) ` 18,110 (c) ` 16,660 (d) ` 17,450 18. What will be the difference between the compound interest and simple interest at the rate of 5% p.a. on an amount of ` 4,000 at the end of two years? (a) ` 10 (b) ` 0 (c) ` 0 (d) Data inadequate 19. If the compound interest accrued on an amount of `14,500 in two year is `4676.5, what is the rate of interest % p.a.? (a) 11 (b) 9 (c) 15 (d) 18 0. The compound interest accrued on an amount of ` 5,500 at the end of three year is ` 8,440.5. What would be the simple interest accrued on the same amount at the same rate in the same period? (a) ` 4]650 (b) ` 5]650 (c) ` 6]650 (d) ` 7]650 1. The simple interest obtained on an amount of ` 45,000 at the end of 4 year is ` 15,00. What would be the approximate compound interest obtained on the same amount at the same rate of interest in the same period? (a) ` 18,44 (b) ` 18,44 (c) ` 16,85 (d) ` 18,566 (e) ` 17,64. The simple interest accrued on a sum of certain principal is ` 1,00 in four year at the rate of 8% p.a. What would be the simple interest accrued on thrice of that principal at the rate of 6% p.a in year?
D-56 NUMERICAL ABILITY 56 (a) `,05 (b) `,05 (c) `,50 (d) `,150. What would be the simple interest accured in 4 years on a principal of `16,500 at the rate of p.c.p.a? (a) 11,560 (b) 10,50 (c) 1,500 (d) 9,980 4. What is the difference between the C.I and S.I. accured on an amount of `1,000 at the end of three years at the rate of 1%? (a) 59,16 (b) 60.4 (c) 495.48 (d) 488. 5. What amount of C.I. can be obtained on an amount of `8,840 at the rate of 5 p.c.p.a at the end of years? (a) 19.16 (b) 16 (c) 184.50 (d) 140 6. What is the C.I accured on an amount of `8500 in two years @ 10 p.c.p.a interest? (a) 1875 (b) 1885 (c) 1775 (d) 1765 7. S.I. accured on an amount in 8 years at the rate of 1 p.c.p.a is `550. What is the principal? (a) 5750 (b) 8500 (c) 5650 (d) 850 8. How much will be the C.I. to be paid on a principal amount of `85,000 after years at the rate of 6 p.c.p.a? (a) 166.6 (b) 166.6 (c) 166.6 (d) 166.6 9. In how many years will `4600 amount to `548 at p.c.p.a simple interest? (a) (b) 5 (c) 6 (d) 4 0. The S.I. accrued on a sum of certain principal years at the rate of 1% per year is `6500. What would be the C.I. accrued on that principal at the rate of 8% per year in years? (a) `1040 (b) `100 (c) `1060 (d) `100 1. Amount of S.I. accrued on an amount of `8,500 in seven years is `940. What is the rate of interest per annum? (a) 10.5 (b) 1.5 (c) 11 (d) 1. Mr. Sharma invested an amount of `5,000 in fixed deposit @ 8% p.a. C.I. for two years. What amount Mr. Sharma will get on maturity? (a) 8540 (b) 9160 (c) 940 (d) 840. S.I. accrued on an amount in eight years @ 11% p.a. is 5700. What was the principal amount? (a) 7000 (b) 8000 (c) 75000 (d) 65000 4. What is C.I. accrued on an amount of `45,000 in two years at the rate of 9 p.c.p.a? (a) 8600 (b) 8565.40 (c) 8464.50 (d) 8540 (e) None of above 5. A principal of `10,000 after years compounded annualy, the rate of interest being 10% p.a. during the first year and 1% p.a. during the second year will amount to: (a) 1,000 (b) 1,0 (c) 1,500 (d) 11,0 6. What is the difference between the S.I. & C.I. on 700 at the rate of 6 p.c.p.a in years? (a) `9.7 (b) 6.8 (c) 1.41 (d). (e) 1.4 7. A sum of money becomes times in 5 years. In how many years will the same sum becomes 6 times at the same rate of SI? (a) 10 years (b) 1 years (c) (e) 1 1 years None of these (d) 1 years 8. A certain sum becomes 7 times itself in 10 years under S.I Find the rate of interest. (a) 1 7 % (b) 0% (c) 10% (d) 1 1 % 9. An amount is lent at y% p.a. S.I for two years. However, is it had been lent at y% p.a. S.I. for x more years, then the interest would have been 5 times the earlier interest. Find the value of y. (a) (b) (c) 4 (d) 5 40. According to a new plan declared by the CSIR Bank, the rate of simple interest on a sum of money is 6% p.a. for the first two years, 8% p.a. for the next three years and 10% p.a for the period beyond first 5 years. Simple interest accrued on a sum for a period of 8 years is `6600. Find the sum. (a) 4,000 (b) 16,000 (c) 10,000 (d) 15,000 (e) None of the above 41. Rahul has borrowed Rs. 0,000 from two money tenders. Or one he had to pay 8% p.a. S.I. and on the other amount he
Simple & compound interest 57 D-57 had to pay 1% p.a. SI. After years, he paid total interest of `5760, find the amount borrowed at 1% p.a. (a) 1,000 (b) 8000 (c) 5000 (d) 10,000 (e) 6000 4. Mohan borrowed `18,000 at 10% p.a. simple interest and then lend it to Sohan at 10% C.I. After years he will earn a profit of (a) 558 (b) 555 (c) 560 (d) 600 (e) None of the above 4 A sum of money borrowed at 10% p.a. for two years at compound interest amounts to `1450. Find the sum borrowed. (a) 10,000 (b) 11,000 (c) 1,000 (d) 1,000 (e) None of the above Answer Key 44. Surya borrowed `5,000 @ 15% p.a. S.I. for 5 years. After 5 years he repaid `15,000 and promised to pay the balance amount after years. Find the amount repayable as final settlement. (a) 6,000 (b),000 (c) 0, (d) 41687.5 (e) None of the above 45. Kamakshi was in need of funds. So, she borrowed? 50,000 at the rate of 8 p.c. p.a. S.I. After years, she was unable to pay back the amount. Therefore, she gave her bike to repay back the loan. Find the price of the bike. (a) 60,000 (b) 58,000 (c) 55,000 (e) 6,000 (e) None of the above 1 (e) 11 (c) 1 (e) 1 (d) 41 (a) (e) 1 (c) (a) (b) 4 (a) (a) 1 (d) (e) (d) 4 (c) 4 (b) 14 (b) 4 (a) 4 (c) 44 (d) 5 (c) 15 (d) 5 (a) 5 (b) 45 (b) 6 (e) 16 (e) 6 (e) 6 (b) 7 (b) 17 (d) 7 (a) 7 (c) 8 (a) 18 (a) 8 (b) 8 (d) 9 (a) 19 (c) 9 (c) 9 (b) 10 (a) 0 (d) 0 (a) 40 (c) ANSWERS & EXPLANATIONS 1. (e) Let the principal be = `x Interest = (19050 x) Now,. (e) Interest Principal = Time Rate (19050 x) x = 9 7x = 1905000 x 17x =1905000 x = 1905000 17 = `15000 Rate Amount = Principal 1 8 = 5000 1+ Time 50001 5 7 7 5000 58` 5 5 CI = ` (58 5000) = 8 `. (a) Interest on ` 1 in 4 years = ` 0.4 Interest on ` in 4 years = ` 40 Interest on ` in 1 year = ` 10 = Principal Time Rate Interest = 450 10 = ` 90 4. (b) Simple Interest = P R T 140081 `0144 Required amount = ` (1400 + 0144) = ` 61544
D-58 NUMERICAL ABILITY 58 5. (c) T R 1. (d) Interest = (5451 1640) = `901 Compound Interest = P 1 1 Interest Rate Principal Time 6 = 15800 1 1 901 = 11% 16405 = 15800 [(1.06) 1)] = 15800 (1.16 1) = 15800 0.16 = ` 195.88 (650 150) 6. (e) Rate = 1506 500 = 17500 = 4% 7. (b) Compound Interest 7 = 0801 1 107 = 080 1 15040000 = 080 0000 504 = 080 0000 = ` 69 (approximate) 8. (a) SI = ` (1710 1050)= ` 460 time = S.I. Principal Rate 5 9. (a) Required Amount = 15000 1 = 460 6 years 1050 4 = ` 1657.50 10. (a) Required Simple Interest = 5760 6 = ` 106.80 148 11. (c) Required Amount = 40001 = 4000 1 = `50880 1. (c) Let the required time = t years Simple interest = (1144 955) = `1907 Simple = P T R 9554t 1907 1907 t = = 5 years 955 4 14. (b) Let the principal be = ` Simple interest = 8 6 = `48 Amount ( + 48) = `148 When the amount is = `148, the principal = ` When amount = `8046, the principal = 8046 = `18950 48 Simple interest = (`8046 18950) = `9096 15. (d) Rate of Interest = (1684 17800) % 178006 = 188400 106800 = 1% 16. (e) 040 Rate 1% 84000 Compound interest 1 = 84000 1 84000 = 11801.95 84000 = ` 401.95 876 17. (d) Amount invested = = ` 17450 8 6 18. (a) Simple interest 19. (c) = 4000 5 = ` 400 Compound interest 5 = 40001 4000 = 4000 105 105 4000 = 4410 4000 = ` 410 Difference = 410 400 = ` 10 r 14500 1 = 14500 + 4676.5 r 19176.5 1 = 59 14500 400
Simple & compound interest 59 D-59 r 1 0 r 1 0. (e) Simple interest principaltimerate 16500416 =`10560 r 1 0 0 r = 15 0 r 0. (d) 5500 1 5500 = 8440.5 r 55001 = 8440.5 + 5500 r 940.5 11 1 0 = 11 5500 10 r 11 1 10 r 1 11 10 r 11 1 1 10 10 4. (a) principaltimerate SI 10001 =`40 time rate CI P1 1 1 10001 1 8 1000 1 5 195 1000 1 1565 67 1000 = `4859.16 1565 r 10 10 Simple interest 5500 10 = = ` 7650 1500 1. (e) Rate = 45000 4 = 8.5% Compound interest 8.5 = 45000 1 45000 4 5. (a) Required difference = 4859.16 40 = `59.16 5 Amt 88401 10.405 CI = Amt Principal = 10.405 8840 =19.405 10 6. (e) Amt = 85001 1085 CI =10850 8500 =1785 4 108.5 = 45000 1 = 45000 0.858 = ` 1764 (approx) 100. (a) Principal = = ` 750 4 8 Simple interest on thrice that principal = 750 6 = ` 05 7. (a) 8. (a) 9. (c) SI 550 Principal 5750 RT 18 6 Amt 85001 1016.6 CI = 1016.6 85000 = 166.6 S.I 88 Time 6 years P R 4600 SI = Amt Principal = 548 4600 = 88
D-60 NUMERICAL ABILITY 60 40 (c) Let the amount deposited be x. S.I 6500 0. (a) Principal 650 RT 18 SI for first years = x 6 1x 1. (d). (b). (d) 4. (c) 5. (b) 6. (b) 7. (c) 8. (d) 9. (b) 8 Amt 6501 790 CI = Amt Principal = 790 650 = 1040 SI 940 Rateof interest 1%p.a. PT 85007 8 Amount 5, 0001 9160 SI 5700 Principal 65000 RT 118 9 Amt 450001 5464.5 CI = 5464.5 45000 = 8464.5 10 1 Amt 10, 0001 1 10 R 6 Difference P 700 6 700 6.8 00 (1) Rate 40% 40 (6 1) Time 1.5years 40 7 1 Rate 1.% 10 P y yp SI p y yp SI yp ( x) 5 yp 5 x, 5 = x = SI for next years = x 8 4x SI for (8 5) i.e. years = So, 1x 4x 0x 6600 66x 6600 x 10 0x 6600 x 10,000 66 41. (a) Let amount borrowed at 8% be x, Let amount borrowed at 1% will be (0,000 x) 4. (a) 4. (c) 44. (d) 45. (b) x 8 (0,000 x) 1 5760 On solving x = 8000 which is the amt.borrowed at 8%. So, amt. borrowed at 1% = 0,000 8000 = 1,000 1800010 SI 5400 10 Amt 180001 958 CI = 958 18000 = 5958 Profit = 5958 5400 = 558 10 110 Amt P1, 1450 P P 1450 1,000 110 110 P 1450 1,000 110 110 5,000155 SI 18750 Amt = 5000 + 18750 = 4750 Balance = 4750 15000 = 8750 875015 SI 197.5 Amt = 8750 + 197.5 = 41687.5 50, 0008 SI 8000 Amt = 50,000 + 8000 = 58,000 or