BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 1

Total Questions: 60

51. Certain sum of money is invested at the rate of 20% simple interest for 5 years after which the amount is invested at the rate of 15% compound interest for 2 years. If the final amount is Rs.7935, then find the initial sum?

Correct Answer: (c) Rs.3000
Solution:

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

Amount earning simple interest = P + P × 20 × 5/100
= 2P

7935 = 2P × (1 + 15/100)²
7935 = 2P × 1.3225
P = 3000

52. A sum of Rs.(P+2000) is invested in SI for 2 years at 20% per annum and also a sum of Rs.(2P-4000) is invested in CI for 2 years at same rate. If the difference between the interest earned is Rs.3200, then find the value of P.

Correct Answer: (a) 12000  
Solution:

Difference between interests = Rs.3200
(2P − 4000)[(1 + (20/100))² − 1] − ((P + 2000) × 2 × 20)/100 = 3200

(2P − 4000)(11/25) − (10(P + 2000))/25 = 3200

P = Rs.12000

53. Ajay invested Rs.56000 in two schemes A and B. Amount invested in scheme A is 33.33% more than B. Ajay earn 8% per annum from A and 10% per annum from B in simple interest. Find total interest earned by Ajay after four years.

Correct Answer: (c) Rs.19840
Solution:

Ratio of amount invested in A and B = 4:3
Amount invested in A = 4/7 × 56000 = 32000
Amount invested in Scheme B = 3/7 × 56000 = 24000

Total interest earned = 32000 × 8% × 4 + 24000 × 10% × 4
= 10240 + 9600 = Rs. 19840

54. Aman invested Rs.1440 for 2 year at the rate of x% in the scheme X at compound interest annually and gets a total amount of Rs.2560. If he invested Rs.3500 in scheme Y at simple interest for 6 years at same rate. Then find the total simple interest earned by Aman from scheme Y.

Correct Answer: (a) Rs.7000  
Solution:

Amount invested by Aman = Rs. 1440
And he gets after 2 years = Rs. 2560

Then, according to the question,
2560 = 1440 × (1 + R/100)²

256/144 = (1 + R/100)²
4/3 = (100 + R)/100

400 = 300 + 3R
R = 33 1/3%

So, the simple interest earned by Aman is,
= 3500 × 100/3 × 6/100
= Rs. 7000

55. The difference between the Simple Interest and Compound Interest incurred on an amount of Rs.1200 in 2 years was Rs.58. Find the rate of interest

Correct Answer: (a) 7%  
Solution:

Difference = Pr²/(100)²
5.88 = 1200 × r²/100 × 100

5.88 × 10000/1200 = r²
r² = 49
r = 7%

56. Anju deposited Rs.24000 in a bank offering 15% Compound interest for 3 years compounded annually. What is the total interest received by Anju?

Correct Answer: (a) Rs.12501  
Solution:Interest received by Anju
= 24000 × ((1 + 0.15)³ − 1)
= Rs.12501

57. Mr.Anish invested Rs.52000 in two different schemes which offers SI at different rate of interest 13% and 8% respectively. If at the end of 2 years he earned overall interest is Rs.11920, then find the sum which is invested at 8% rate of interest?

Correct Answer: (b) Rs.16000  
Solution:

Let amount invested in 1st scheme be x,
Amount invested in 2nd scheme be 52000 − x

It is given that,
x × 2 × 13/100 + (52000 − x) × 8 × 2/100 = 11920

26x/100 + 16(52000 − x)/100 = 11920

x = Rs.36000

Therefore amount invested in 2nd scheme
= 52000 − 36000 = Rs.16000

58. The difference between the compound interest and simple interest for the sum of Rs.25000 at the end of two years at the rate of 20% per annum?

Correct Answer: (e) None of these
Solution:Difference = (25000 × 20 × 20)/(100 × 100)
= Rs.1000

59. Arun invested Rs.5000 in a bank at Simple interest for 2 years and receives an interest of Rs.500. What is the rate of interest?

Correct Answer: (b) 5%  
Solution:

Given that, SI = Rs.500, n = 2 years and P = Rs.5000

SI = Pnr/100

r = (100 × SI)/(P × n)
= (100 × 500)/(5000 × 2)
= 5%

60. If Rs.11750.4 amount is received for lending Rs.x for 3 years at 20% per annum compound interest, find the value of x?

Correct Answer: (b) Rs.6800  
Solution:

CA = P × (1 + r/100)ⁿ

11750.4 = x × (1 + 20/100)³

x = 6800