BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 2

Total Questions: 60

51. Grace invested a certain amount in compound interest at 20% compounded half yearly for one year. If the compound interest obtained by Grace is Rs.840, then find the total amount invested by Grace?

Correct Answer: (d) Rs.4000  
Solution:

Let the total amount invested by Grace = a

The rate of interest (half yearly) = 20%/2 = 10%

a × {(1 + 10/100)² − 1} = 840

a × (121/100 − 1) = 840

a = 840 × 100/21

a = 4000

52. Soniya invested Rs.6500 in simple interest at 40% per annum for n years. After n years, the interest obtained by Soniya is five times more than the amount invested. Find the value of n?

Correct Answer: (a) 15  
Solution:

The amount invested by Soniya = Rs. 6500

6500 × 40 × n/100 = 6 × 6500

n = 15

53. Bharat invested Rs.15000 for 2 years at R% per annum simple interest. Sindhu invested the same amount as invested by Bharat for 2 years at R% per annum compound interest. What is the amount received by Sindhu, if the difference between the interest earned by Bharat and Sindhu is Rs.600?

Correct Answer: (b) Rs.21600  
Solution:

PR²/100² = Difference of interest

⇒ 15000 × R²/100² = 600

⇒ R = 20%

Amount received by Sindhu = 15000 × (1 + 20/100)²
= Rs. 21600

54. Meena invests Rs.x in a compound interest scheme at the rate of 20% per annum for 2 years, Nila invests Rs.y in the same compound interest scheme at the rate of 20% per annum for 2 years. The total interest received by Meena and Nila is Rs.4092. If Nirmal invests Rs.2x in a simple interest scheme at the rate of 10% per annum for 2 years and Rani invests Rs.2y in a simple interest scheme at the rate of 15% per annum for 3 years and total interest received by Rani and Nirmal is Rs.5970, find the value of x?

Correct Answer: (b) Rs.4800  
Solution:

CI = P × (1 + R/100)ⁿ − P
SI = P × N × R/100

4092 = x × (1 + 20/100)² − x + y × (1 + 20/100)² − y

4092 = 0.44x + 0.44y

x + y = 9300 …..(1)

5970 = (2x × 10 × 2/100) + (2y × 15 × 3/100)

59700 = 40x + 90y

4x + 9y = 59700 …..(2)

5y = 22500
y = 4500

x = 9300 − 4500 = Rs.4800

55. Directions (55 - 59): Study the following information carefully and answer the questions given below.

The table shows the five different persons principal, number of years and rate of interest. Some values missing in the table find the values according to the question.

Person

P

N Year

R%

A

40000

2

15

B

50000

3

-

C

-

4

-

D

-

4

15

E

76000

2

-

Ques. Rate of interest is increased by 5% and compounded half yearly. What will be the amount after given period for A?

Correct Answer: (d) 58564  
Solution:

R = 15 + 5 = 20%

Amount = P (1 + (R/2)/100)²ⁿ

= 40000 × (1 + 10/100)⁴

= 40000 × 110/100 × 110/100 × 110/100 × 110/100

= 58564

56. The difference between simple interest and compound interest is Rs.125 for 2 years. What is the interest amount for B if compounded annually?

Correct Answer: (a) 7881.25  
Solution:

Difference between CI and SI for 2 years = PR²/100² = 125

50000 × R²/10000 = 125

R = 5%

Amount = P (1 + (R)/100)ⁿ

= 50000 × 105/100 × 105/100 × 105/100

= 57881.25

Compound interest = 57881.25 − 50000 = 7881.25

57. If the simple interest for 1 year is 640, the amount becomes 6560 after given years. What is the amount invested and rate of interest for C?

Correct Answer: (c) 16%
Solution:

N = 4, 640 × 4 = 2560

P = 6560 − 2560 = 4000

R = 100 × 640/4000 × 1 = 16%

58. The principal of D is increased by 12% for 1st year and by given percentage for the rest of the years so that it amounts to 340676. What is difference between principal of D and B?

Correct Answer: (e) None of these
Solution:

P × 112/100 × 115/100 × 115/100 × 115/100 = 340576

P = 200000

Difference between D and B = 150000

59. Person E invested his principal amount in two equal parts, one at simple interest and another one at compound interest for the given years. If the interest received from SI and CI are Rs.5320 and Rs.7980 respectively. What is the rate of interest for SI and CI according to E?

Correct Answer: (d) 7%, 10%  
Solution:

(d): SI:
P = 38000

SI = PNR/100

38000 × 2 × R/100 = 5320

R = 7%

CI:
P = 38000

P + CI = P × (1 + r/100)²

38000 + 7980 = 38000 × (1 + r/100)²

(1 + r/100)² = 45980/38000 = 121/100

1 + r/100 = 11/10

⇒ r = 10%

60. A bank decides to lend Rs.10 crore through three types of loans namely Personal loan, Home loan and Car loan. The interest rates per annum as well as the bad debt as a percentage of the money lent in each type of mentioned loan is shown in the table given below. Bad debt is a debt that does not give any return and cannot be recovered.

Loan

Interest Rate

Bad debt

Personal

15%

5%

Home

10%

3%

Car

9%

2%

Ques. In which of the following ways should the Bank lend Rs.10 crore such that it maximizes it’s return on the money lent for a period of 1 year?

Correct Answer: (e) Bank should lend Rs. 10 crore as personal loan
Solution:

Option (a):
The total amount at the end of 1 year,
⇒ 0.97 × 1.1 × 5 + 1.15 × 3 × 0.95 + 2 × 1.09 × 0.98
= Rs. 10.7489 crore.

Option (b):
The total amount at the end of 1 year,
⇒ 1.15 × 0.95 × 5 + 1.09 × 0.98 × 5 = Rs. 10.8035 crore.

Option (c):
The total amount at the end of 1 year,
⇒ 0.33 × 10 × (1.15 × 0.95 + 1.1 × 0.97 + 1.09 × 0.98) = Rs. 10.759 crore.

Option (d):
The total amount at the end of 1 year,
⇒ 10 × 1.09 × 0.98 = Rs. 10.682 crore.

Option (e):
The total amount at the end of 1 year,
⇒ 10 × 1.15 × 0.95 = Rs. 10.925 crore.

Hence, option (e) is the correct answer.