CPT Section D Quantitative Aptitude Chapter 4 J.P.Sharma

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1 CPT Section D Quantitative Aptitude Chapter 4 J.P.Sharma

2 A quick method of calculating the interest charge on a loan. Simple interest is determined by multiplying the interest rate by the principal by the number of periods. SI = P x I x N Where: P is the loan amount I is the interest rate N is the duration of the loan, using number of periods

3 Simple interest is called simple because it ignores the effects of compounding. The interest charge is always based on the original principal, so interest on interest is not included. This method may be used to find the interest charge for short-term loans, where ignoring compounding is less of an issue.

4 Interest that accrues on the initial principal and the accumulated interest of a principal deposit, loan or debt. Compounding of interest allows a principal amount to grow at a faster rate than simple interest, which is calculated as a percentage of only the principal amount.

5 The more frequently interest is added to the principal, the faster the principal grows and the higher the compound interest will be. The frequency at which the interest is compounded is established at the initial stages of securing the loan. Generally, interest tends to be calculated on an annual basis, although other terms may be established at the time of the loan.

6 A = P (1+ i ) n here i = R 100 P = principal A = amount n = number of years.

7 Compound interest = Amount Principal = P[ (1+i) n-1] Case 1 : if interest is calculated half yearly or semi-annually i = R, n= 2 times 200 Case 2 : if interest is calculated quarterly i = R, n= 4 times 400 Case 3 : if interest is calculated monthly i = R, n= 12 times 1200 Note : the above mentioned cases will be applicable only when time is given in years.

8 FINAL VALUE = INITIAL VALUE x (1± i 1 ) (1± i 2 ) For example :- Population of a town is 100,000. it increases every year by 2%. Find how much will be the population of the town after 3 years Solution :- Initial value = Final value? i = 2/100 or 0.02 n = 3 years Therefore Final Value = x ( ) 3 = i.e Since population can not be in decimal.

9 Lets have one more example Mr. Shyam purchased 1 kg. of gold for 30 lacs. In the first year of his purchase the price of gold inflated to 10%, whereas in the next 2 years it deflated by 5% and 4 % respectively. Calculate the final value of his investment in gold. Solution :- Final Value = 30,00,000 (1+ 0.1) ( ) (1-0.04) = 30,00,000 x =

10 If interest is charged on the principal for more than once in an year, in such case rate of interest is compounded and interest is calculated on annual base, such rate of interest that comes after compounding is termed as effective rate of interest. Formula : E = [ (1+i) n 1 ] x 100 For example Interest to be paid on Rs. 3% p.a.but to be compounded half yearly Then the effective rate of interest according to the formula will be E = [ ( /200) 2 1 ] x 100 = %

11 A financial product sold by financial institutions that is designed to accept and grow funds from an individual and then, upon annuitization, pay out a stream of payments to the individual at a later point in time. Annuities are primarily used as a means of securing a steady cash flow for an individual during their retirement years.

12 Annuities can be structured according to a wide array of details and factors, such as the duration of time that payments from the annuity can be guaranteed to continue. Annuities can be created so that, upon annuitization, payments will continue so long as either the annuitant or their spouse is alive. Alternatively, annuities can be structured to pay out funds for a fixed amount of time, such as 20 years, regardless of how long the annuitant lives.

13 Annuities can be structured to provide fixed periodic payments to the annuitant or variable payments. The intent of variable annuities is to allow the annuitant to receive greater payments if investments of the annuity fund do well and smaller payments if its investments do poorly. This provides for a less stable cash flow than a fixed annuity, but allows the annuitant to reap the benefits of strong returns from their fund's investments. The different ways in which annuities can be structured provide individuals seeking annuities the flexibility to construct an annuity contract that will best meet their needs.

14 Annuity in simple terms can be re defined as equated amounts to be paid or received in equal interval of time It majorly can be bi-furcated into two types Regular or Ordinary Immediate or Due

16 Each payment of an ordinary annuity belongs to the payment period preceding its date, while the payment of an annuity-due refers to a payment period following its date. The meaning of the above statement may not be immediately obvious until we look at it graphically...

17 In simple terms it can be defined as, when amounts are paid or received at the end of the time period Future Value Present Value A (1+i) n - 1 A (1+i) n - 1 i i(1+i) n

18 In simple terms it can be defined as, when amounts are paid or received in the beginning of the time period Future value A (1+i) n - 1 (1+i) i Present Value A (1+i) n 1 + A i(1+i) n

19 1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: A.Rs. 650 B.Rs. 690 C.Rs. 698 D.Rs. 700

20 A.Rs B.Rs C.Rs D.Rs E.None of these

21 A.Rs B.Rs C.Rs D.Rs E.None of these

22 A.3.5 years B.4 years C.4.5 years D.5 years

23 A.3.6 B.6 C.18 D.Cannot be determined E.None of these

24 A.3% B.4% C.5% D.6% E.None of these

25 A.10% B.10.25% C.10.5% D. None of these

26 A.5% B.7% C.71%8 D.10%

27 A.3.6% B.4.5% C.5% D.6% E.None of these

28 A.Rs B.Rs. 10,000 C.Rs. 15,000 D.Rs. 20,000

29 A.5% B.8% C.12% D.15%

30 A.1 : 3 B.1 : 4 C.2 : 3 D.Data inadequate E.None of these

31 A.Rs. 35 B.Rs. 245 C.Rs. 350 D.Cannot be determined E.None of these

32 A.Rs B.Rs. 125 C.Rs. 150 D.Rs

33 A. 2% B.5% C.8% D.10%

34 A. 3.5 years B.4 years C.4.5 years D.5 years

35 A.5% B.7% C.8% D.10%

36 A B C D

37 A. 3.6 B. 6 C.18 D. Cannot be determined

38 A. Rs B.Rs C.Rs D.Rs.5300

39 1. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs each on 1 st January and 1 st July of a year. At the end of the year, the amount he would have gained by way of interest is: A.Rs. 120 B.Rs. 121 C.Rs. 122 D.Rs. 123

40 A.625 B.630 C.640 D.650

41 A.Rs B.Rs C.Rs D.Rs E.None of these

42 A.Rs B.Rs C.Rs D.Rs. 8.30

43 A.2 B.2.5 C.3 D.4

44 A.Rs B.Rs C.Rs D.Rs E.None of these

45 A.6% B.6.5% C.7% D.7.5%

46 A.3 B.4 C.5 D.6

47 A.Rs B.Rs C.Rs D.None of these

48 A.6.06% B.6.07% C.6.08% D.6.09%

49 A.Rs B.Rs C.Rs D.Rs. 2000

50 A.Rs B.Rs. 52 C.Rs D.Rs. 60

51 A.Rs B.Rs. 3 C.Rs D.Rs. 4 E.None of these

52 A.8 B.10 C.12 D.Cannot be determined E.None of these

53 A.Rs. 400 B.Rs. 500 C.Rs. 600 D.Rs. 800

54 1. 13% % 3. 15% 4. 11% 5. None of these

55 1. Rs Rs Rs Rs Rs. 9500

56 1. 11 years years years years years

58 1. Rs Rs Rs Rs Rs.600

You expect annual interest rates will be 8 percent over that time

60 1. You want to buy an ordinary annuity that will pay you $4,000 a year for the next 20 years. You expect annual interest rates will be 8 percent over that time period. The maximum price you would be willing to pay for the annuity is closest to A.$32,000 B.$39,272 C.$40,000 D.$80,000

61 A.$34,898 B.$40,171 C.$164,500 D.$328,282

62 A. fall B. rise C. remain unchanged D.cannot be determined without more information.

4. For $1,000 you can purchase a 5-year ordinary annuity that will pay you a yearly payment of $263.80 for 5 years.

63 4. For $1,000 you can purchase a 5-year ordinary annuity that will pay you a yearly payment of $ for 5 years. The compound annual interest rate implied by this arrangement is closest to A.8 percent B.9 percent C.10 percent D.11 percent

64 A.$2,674. B.$2,890. C.$3,741. D.$4,020.

65 A.The present value of an annuity due is greater than the present value of an ordinary annuity B.The present value of an ordinary annuity is greater than the present value of an annuity due C.The present value of both the annuities is the same D. None of these.

66 A.$500 B.$600 C.$700 D.$800

67 A.$2, B.$2, C.$2, D.$2,500.00

68 A.Rs.1275 B. Rs.1383 C. Rs.1352 D. Rs.1287 E. Rs.1250

69 A. Rs.14,000 B. Rs.13,684 C. Rs.15,600 D. Rs.14,320 E. None of these

70 A. $52,000 B.$93,219 C.$99,061 D.$915,240

71 A.Rs B. Rs c. Rs D. None of these

72 A B C D

73 A. Rs.0.83 B. Rs 0.91 C. Rs D.Rs.0.79

74 A. Rs B. Rs C. Rs D. Rs

75 SINKING FUND A fund formed by periodically setting aside money for the gradual repayment of a debt or replacement of a wasting asset. A fund into which a company sets aside money over time, in order to retire its preferred stock, bonds or debentures. In the case of bonds, incremental payments into the sinking fund can soften the financial impact at maturity. Investors prefer bonds and debentures backed by sinking funds because there is less risk of a default.

Some bonds do not pay interest, but all bonds require a repayment of principal. When an investor buys a bond, he/she becomes a creditor of the issuer.

76 A debt instrument issued for a period of more than one year with the purpose of raising capital by borrowing. Generally, a bond is a promise to repay the principal along with interest (coupons) on a specified date (maturity). Some bonds do not pay interest, but all bonds require a repayment of principal. When an investor buys a bond, he/she becomes a creditor of the issuer. However, the buyer does not gain any kind of ownership rights to the issuer, unlike in the case of equities. On the hand, a bond holder has a greater claim on an issuer's income than a shareholder in the case of financial distress (this is true for all creditors).

77 A sinking fund is created for reducing debenture worth Rs at the end of 25 years. How much provision needs to be made out of profits each year provided sinking funds investments can earn 4% p.a. A. Rs B. Rs C. Rs D. Rs

78 A. Rs B. Rs C. Rs D. Rs

DAILY QUESTIONS. 24 th MAY 18 QUANT COMPOUND INTEREST

DAILY QUESTIONS. 24 th MAY 18 QUANT COMPOUND INTEREST DAILY QUESTIONS 24 th MAY 18 QUANT Q.1) Which amongst the following two offers is the better one? (1) investing an amount compounded annually at 1% per annum for 100 years. (2) investing the amount compounded