BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 1

Total Questions: 60

21. Two equal sums are lent at the same time to two different borrowers at 10% and 5% simple interest respectively. The former is received 3 years earlier than the latter, and the amount received in the latter case is Rs. 7000. If the amount returned by the second borrower is Rs. 500 less than the amount obtained from the first borrower, find the sum lent to each borrower and the time taken by the second borrower to return the money.

Correct Answer: (a) Rs. 5000, 8 years
Solution:

Let the sum lent to both borrowers = Rs. x.
Let the time taken by the second borrower to return the money = n years.

x + (x × n × 5)/100 = 7000
x + (x × (n-3) × 10)/100 = 7500

Solving these two equations, x = Rs. 5000, n = 8 years.
Hence, option a.

22. A person invested some amount at the rate of 15% simple interest and a certain amount at the rate of 18% simple interest. He received yearly interest of Rs. 360. But if he had interchanged the amounts invested, he would have received Rs. 6 more as interest. How much did he invest initially at 15% simple interest initially?

Correct Answer: (d) Rs. 1200  
Solution:

Amount invested at 15% = Rs. x
Amount invested at 18% = Rs. y

360 = x × 15/100 × 1 + y × 18/100 × 1
36000 = 15x + 18y

and 366 = x × 18/100 × 1 + y × 15/100 × 1
36600 = 18x + 15y

solving both equations,
x = 1200, y = 1000
Hence, option d.

23. Sonam took a loan of Rs. 5 lakhs for her 4 years course of B Tech. The rate of interest is such that she would be charged 10% per annum at Compound Interest during her course and 12% CI after the completion of course. She returned half of the amount which had to be paid on the completion of her studies and the remaining after 2 years. What is the total amount returned by Sonam (approximately)?

Correct Answer: (e) Rs. 8.25 lakhs
Solution:

Amount which is to be returned on completion of the course
= 5 × (1.1)⁴
= 7.32 lakhs (approx.)

But she returns only half, i.e. 3.66 lakhs.
Amount which is returned after 2 years of completion of the course = 3.66 × (1.12)² = 4.59 lakhs.

Total amount returned = 3.66 + 4.59 = Rs. 8.25 lakhs

24. A person deposited his money in a bank which offers him simple interest at the rate of 12.2% per annum. He deposited Rs 28000. After every three years he adds the amount he earned from the interest to his principal amount. Find the total amount (approximate) after 9 years?

Correct Answer: (b) Rs. 71369  
Solution:

Deposited amount = Rs 28000
Rate = 12.2%
For 3 years:
SI = 28000 × 12.2 × 3/100
SI = 10248

After 3 years
Principal amount = (28000 + 10248)
= Rs 38248

Rate: 12.2%
For next 3 years:
= 38248 × 12.2 × 3/100
= Rs 13998.7

After years: (38248 + 13998.7)
= Rs 52246.7

For next 3 years:
= (52246.7 × 12.2 × 3/100) = Rs 19122.3

After 9 years:
Amount = Rs 71369
Hence option b.

25. A maid borrowed money from 2 houses (X and Y) she works in. From X she borrowed money at an interest rate of 15% and from Y at the rate of 18%. The total money she borrowed was Rs. 24000. She paid Rs. 4050 as an interest in addition to the amount borrowed after 1 year. Find how much money she borrowed at 18% interest rate?

Correct Answer: (c) Rs. 15000
Solution:

Let the Sum at 15% be Rs.x then at 18% be Rs (24000 - x)

P1 = x R1 = 15
P2 = (24000 - x) R2 = 18

After 1 year T = 1
(P1 × T × R1)/100 + (P2 × T × R2)/100 = 4050

(x × 1 × 15)/100 + ((24000 - x) × 1 × 18)/100
= 4050

15x + 432000 - 18x = 405000
x = 9000

Money borrowed at 15% = 9000
Money borrowed at 18% = (24000 - 9000)
= 15000

Hence, option c.

26. Shahrukh lends Rs. 725 to a friend in January 2016 at a certain rate. In September 2016 a sum of Rs. 325 more is given to same person at same rate. On 31st December, Rs. 33.5 is earned from interest from the loan. Find the original rate of interest?

Correct Answer: (c) 4.02%
Solution:

Let the rate be = r%

The original rate of interest for 1 year and interest for 1/3 years.

(725 × r × 1)/100 + (325 × r × 1)/(100 × 3) = 33.5

(2175 + 325) × r = 33.50 × 100 × 3
r = 10050/2500
= 4.02

Original rate = 4.02%
Hence, option c.

27. A person invested two different amounts in two different plans. One of the plans returns 10% compound interest per annum (compounded annually) and the other plan returns 10% simple interest per annum. If the total compound interest earned in two years from the former plan is equal to the simple interest earned in fours in latter plan, what was the respective ratio of amounts invested in the two plans?

Correct Answer: (b) 40:21  
Solution:

Let the amount invested in the scheme returning compound interest = P

Let the amount invested in the scheme returning simple interest = Q

According to question,
P × [(1 + 0.1)² - 1] = Q × (0.1) × 4

=> P × (1.21 - 1) = Q × (0.4)
=> P/Q = (0.4)/(0.21) = 40:21

Hence, option b.

28. A person invests some amount at 5% per annum and another amount at 9% per annum. If two-third of the first amount is equal to the four-fifth of the second amount, and total interest earned in 2 years is Rs. 2070, what was the total sum invested?

Correct Answer: (c) Rs. 15180
Solution:

Let the first amount be ‘x’ and the second amount be ‘y’

(2/3) × x = (4/5) × y
=> x = 1.2y

Total interest earned in 2 years = 2070

or, (x × 5 × 2)/100 + (y × 9 × 2)/100 = 2070

or, (1.2y × 5 × 2)/100 + (y × 9 × 2)/100 = 2070 × 100/2

or, 15y = 2070 × 200 => y = 6900

So, x = 1.2y = 6900 × 1.2 = 8280

Therefore, total sum invested = 6900 + 8280
= Rs. 15180

Hence, option c.

29. Shikha invested a total of Rs. 1500 in two different schemes offering simple interest of 6% and 4% respectively. In two years time, the scheme offering higher interest rate gives Rs. 100 more interest than the scheme offering the lower rate. What was the ratio of amount invested at higher interest rate to the other amount?

Correct Answer: (b) 11:4  
Solution:

Let the sum invested by Shikha in the Scheme offering higher interest rate be ‘x’

So, Sum invested by Shikha in another scheme = (1500 - x)

Thus, (x × 6 × 2)/100 - [(1500 - x) × 4 × 2]/100
= 100

(12x/100) + (8x/100) - 120 = 100

On solving x = Rs. 1100

Another amount = 1500 - 1100 = Rs. 400

Thus, the required ratio = 11 : 4

Hence, option b

30. Shaifali invested a certain sum of money in scheme X for 5 years and double of that amount in scheme Y for 3 years. Both the schemes offer simple interest at the rate of 8% pa. The difference between the amount received (including interest) from both the schemes was Rs 12960. How much did Shaifali invest in scheme X?

Correct Answer: (b) Rs.12000  
Solution:

Amount invested in scheme ‘X’ is ‘x’ and Amount invested in scheme ‘Y’ is ‘2x’

So, 12960 = 2[(x × x × 24)/100] - [x + 40x/100]

Or, 248x - 140x = 1296000

Or, x = 12000

Hence, option b.