BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 2

Total Questions: 60

31. Mohit borrowed Rs ‘P’ from a friend at simple interest of 16% p.a. He then immediately gave this money to Ram at compound interest of 20% p.a., compounded annually for 2 years. If at the end of two years, he earned a profit of Rs. 6,000, then find the value of ‘P’.

Correct Answer: (d) 50,000  
Solution:

ATQ:
[P × {(1.2)² − 1}] − [(P × 16 × 2)/100] = 6000

Or, 0.44P − 0.32P = 6000

Or, 0.12P = 6000

So, P = 50,000

Hence, option d.

32. Ram invested equal sums in two schemes ‘A’ & ‘B’ for two years each. Scheme ‘A’ offers simple interest of 12% p.a. whereas scheme ‘B’ offers compound interest (compounded annually) of 12% p.a. If the interest received from scheme ‘A’ is Rs. 4,800, then find the amount received from scheme ‘B’.

Correct Answer: (d) Rs. 25,088  
Solution:

Let the sum invested by Ram in each scheme be Rs. ‘P’

According to the question,

Or, 4800 = {(P × 12 × 2)/100}

Or, P = 20,000

Amount received from scheme ‘B’ = P × (1 + (R/100))ᵀ

Amount received from scheme ‘B’ = 20000 × (1 + (12/100))²

Amount received from scheme ‘B’ = 20000 × (1.12)²

= Rs. 25,088

Hence, option d.

33. ‘A’ lent some amount of money to ‘B’ at certain rate of simple interest per annum. After 8 years ‘B’ returned twice the amount given by ‘A’ to him. Find the rate of interest at which ‘A’ lent the amount to ‘B’.

Correct Answer: (c) 12.5% p.a.
Solution:

Let the amount of money lent by ‘A’ to ‘B’ be Rs. ‘P’.

Let the rate of interest be ‘R%’ p.a.

Simple interest received = 2P − P = Rs. ‘P’

So, P = {(P × R × 8)/100}

Or, R = [(P × 100)/(P × 8)] = 12.5% p.a.

Hence, option c.

34. Find the difference between the simple interest received on Rs. 6,450 invested at the rate of 10% p.a. for two years and the compound interest received on Rs. 5,000 invested at the rate of 20% p.a., compounded annually for two years.

Correct Answer: (c) Rs. 910
Solution:

Simple interest received = {(6450 × 10 × 2)/100}
= Rs. 1,290

Compound interest received = 5000 × {(1 + (20/100))² − 1}

= 5000 × {(1.2)² − 1} = 5000 × (1.44 − 1) = 5000 × 0.44 = Rs. 2,200

Required difference = (2200 − 1290) = Rs. 910

Hence, option c.

35. When a certain sum is invested for 5 years at simple interest of 9% p.a., the interest earned is Rs. 5,670. If the same sum was invested for 2 years at compound interest of 10% p.a., what would be the total amount received?

Correct Answer: (e) Rs. 15,246
Solution:

Let the amount invested = Rs. ‘Y’

ATQ:
Y × 5 × 9 ÷ 100 = 5670

Or, Y = 5670 ÷ 0.45 = 12600

So, total amount received upon investing Rs. 12,600 for 2 years at 10% p.a.

= 12600 × {(1 + (10/100))²} = 12600 × (110/100)²

= Rs. 15,246

Hence, option e.

36. Difference between compound interest (compounded annually) and simple interest on a certain sum, invested at 20% p.a. for 3 years is Rs. 576. Find the sum.

Correct Answer: (e) Rs. 4,500
Solution:

Let the sum invested be Rs. ‘p’

Difference between compound interest (compounded annually) and simple interest

= p × (r/100)² × {(300 + r)/100}

576 = p × (20/100)² × {(300 + 20)/100}

Or, 576 = (p/25) × (16/5)

Or, 36 = (p/125)

Required sum = Rs. 4,500

Hence, option e.

37. Ram invested some amount in scheme ‘A’ and scheme ‘B’ for 4 years and 5 years, respectively. Scheme ‘A’ and Scheme ‘B’ are offering simple interest at 6% p.a. and 8% p.a., respectively. If interest received from both the schemes is same, then find the ratio between amounts invested in scheme ‘A’ and ‘B’

Correct Answer: (c) 5:3
Solution:

Let the amount invested in schemes ‘A’ and ‘B’ be Rs. ‘a’ and Rs. ‘b’, respectively.

Simple interest received from scheme ‘A’ = {a × 6 × (4/100)} = Rs. (24a/100)

Simple interest received from scheme ‘B’ = {b × 8 × (5/100)} = Rs. (40b/100)

ATQ:
(24a/100) = (40b/100)

Or, (a/b) = (40/24) = (5/3)

Therefore, required ratio = 5:3

Hence, option c.

38. Suman invested a certain sum in scheme ‘A’ and scheme ‘B’ in the ratio 2:1, respectively. Scheme ‘A’ offers simple interest at 30% p.a. and scheme ‘B’ offers compound interest (compounded annually) at 20% p.a. Find the total sum invested by Suman in both the schemes together if the difference between interests earned from the two schemes after 3 years is Rs. 1,608.

Correct Answer: (b) Rs. 4,500  
Solution:

Let the total sum invested by Suman in both schemes together be Rs. ‘30x’

So, amount invested in scheme ‘A’ = 30x × (2/3)
= Rs. ‘20x’

And, amount invested in scheme ‘B’ = (30x − 20x) = Rs. ‘10x’

Simple interest received from scheme ‘A’ = {(20x × 30 × 3)/100} = Rs. ‘18x’

Compound interest received from scheme ‘B’
= 10x [(1 + (20/100))³ − 1] = 10x (91/125)
= Rs. (182x/25)

According to question:
18x − (182x/25) = 1608

Or, 9x − (91x/25) = 804

Or, {(225x − 91x)/25} = 804

Or, (134x/25) = 804

Or, x = 150

Total sum invested by Suman = 30 × 150 = Rs. 4,500

Hence, option b.

39. A man invested Rs. 10,000 in three different schemes in the ratio of 4:3:3. He invested the largest share at simple interest of 20% p.a. and other parts at the simple interest of 18% p.a. and 24% p.a. Find the total interest earned by the man at the end of 4 years.

Correct Answer: (d) Rs. 8,240  
Solution:

Amount invested at 20% p.a. = 10000 × (4/10)
= Rs. 4,000

Amount invested at 24% p.a. and 18% p.a.
= (10000 − 4000) ÷ 2 = Rs. 3,000 each

So, total interest earned
= {(4000 × 20 × 4)/100} + {(3000 × 18 × 4)/100} + {(3000 × 24 × 4)/100}

= 3200 + 2160 + 2880 = Rs. 8,240

Hence, option d.

40. A man invested a sum at compound interest of 40% p.a. compounding semi-annually for 18 months. If the amount received by the man at the end of 18 months is Rs. 25,920, then find 40% of the sum invested by the man.

Correct Answer: (d) Rs. 6,000  
Solution:

Let the sum invested be Rs. ‘P’

Effective rate of interest = 40 ÷ 2 = 20% p.a.

Effective terms = (18/12) × 2 = 3 terms

ATQ:
25920 = P × (1.2)³

Or, P = 25920 × (10/12) × (10/12) × (10/12)

So, P = 15,000

Therefore, required sum = 0.4 × 15000 = Rs. 6000

Hence, option d.