BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 3

Total Questions: 60

1. A man invested a sum at compound interest of 20% p.a., compounded annually. At the same time, he invested another sum in two different parts in a scheme, where he invested 40% of the sum at simple interest of (92/3)% p.a. and the rest at simple interest of 20% p.a. If the total interest earned by the man at the end of 3 years after making the first investment is Rs. 1,09,200, then how much more amount the man would’ve earned had he invested the whole amount on simple interest of 40% for three years?

Correct Answer: (c) Rs. 70,800  
Solution:

Let the amount invested at compound interest be Rs. ‘y’ and the amount invested at simple interest be Rs. ‘5x’

So, amount invested at (92/3)% p.a. simple interest =
5x × 0.4 = Rs. ‘2x’

And, amount invested at 20% p.a. simple interest =
5x × 0.6 = Rs. ‘3x’

ATQ:
{(2x × (92/3) × 3)/100} + {(3x × 20 × 3)/100} + [y × {(1.2)³ − 1}] = 109200

(46x/25) + (9x/5) + (0.728y) = 109200

(46x + 45x)/25 + 0.728y × 25 = 109200 × 25

91x + 18.2y = 109200 × 25

5x + y = 6000 × 25

So, 5x + y = 150000

So, the amount invested by the man = Rs. 1,50,000

So, interest the man would’ve earned had he invested the whole amount at 40% simple interest =

{(150000 × 40 × 3)/100} = Rs. 1,80,000

So required profit = 180000 − 109200 = Rs. 70,800

Hence, option c.

2. Rohit borrowed some money at compound interest from a bank that lends in a special manner. For first two years, the rate of interest is 5% p.a. for next two years it increases to 10% p.a. Similarly, for the next two years the interest becomes 20% p.a. If Rohit borrowed the money for 6 years, and paid Rs. 11,51,245 as interest, then find the amount borrowed by him. (The interest was always compounded annually.)

Correct Answer: (d) Rs. 12,50,000
Solution:

Let the principle borrowed be Rs. ‘P’

ATQ:
1151245 + P = P × (1.05)² × (1.1)² × (1.2)²

1151245 = 1.920996P − P

1151245 = 0.920996P

P = Rs. 12,50,000

Hence, option d.

3. Ajay invested Rs. 32,000 in scheme ‘A’ which offers compound interest (compounded half yearly) at 50% p.a. for 12 months. Then he reinvested the interest earned from scheme ‘A’ in another scheme ‘B’ which also offers compound interest (compounded annually) at ‘r%’ p.a. for 3 years. This way, he earned a total interest of Rs. 31,104 after 5 years. Find the value of ‘r’.

Correct Answer: (d) 20%  
Solution:Effective rate of interest for scheme ‘A’ = 50/2 = 25%

And, time period = 2 terms, where each term consist of 6 months

Compound interest earned from scheme ‘A’
= 32000 × {(1 + (25/100))² − 1} = 32000 × (9/16)
= Rs. 18,000

Interest earned from scheme ‘B’ = 31104 − 18000
= Rs. 13,104

Now, according to the data given:
13104 = 18000 × {(1 + (r/100))³ − 1}

(13104/18000) = {(1 + (r/100))³ − 1}

(91/125) = {(1 + (r/100))³ − 1}

{(91 + 125)/125} = {1 + (r/100)}³
(216/125) = {1 + (r/100)}³
(6/5)³ = {1 + (r/100)}³
(6/5) = {1 + (r/100)}
(1/5) = (r/100)
So, r = 20.

4. Sudhanshu invested Rs. 25920 in scheme ‘A’ at a rate of ‘R%’ p.a. compounded 5 monthly. After 10 months, he deposited 80% of the amount received from scheme ‘A’ in scheme ‘B’ offering a simple interest of 15% p.a. After 18 more months, he spent Rs. 5052.1 from the amount received from scheme ‘B’ and invested the rest in scheme ‘C’ at a rate of 20% p.a. compounded quarterly. Total time for which he made investment in scheme ‘C’ is 9 months and amount received by him from scheme ‘C’ is Rs. 27783. Find the value of ‘R’.

Correct Answer: (c) 16(2/3)
Solution:

Let a = (5R/12)% per annum
So, amount received from scheme ‘A’ = 25920 × {(1 + a/100)²}

Amount invested in scheme ‘B’ = 0.80 × 25920 × {(1 + a/100)²}
= Rs. 20736{(1 + a/100)²}

Amount received from scheme ‘B’ = 20736{(1 + a/100)²}[1 + 0.15 × (18/12)]
= 25401.6{(1 + a/100)²}

Amount invested in scheme ‘C’ = [25401.6{(1 + a/100)²} − 5052.1]

Time for which investment was made in scheme ‘C’
= 40 − 10 − 18 = 12 months

Desired rate = 20 × (1/4) = 5% per quarter

So, 1.05 × 1.05 × 1.05 × [25401.6{(1 + a/100)²} − 5052.1] = 27783

[25401.6{(1 + a/100)²} − 5052.1] = 24000

[25401.6{(1 + a/100)²}] = 29052.1

(1 + a/100)² = 5929/5184

1 + a/100 = 77/72

a/100 = 5/72

So, R = (5/72) × (12/5) × 100 = (100/6) = 16(2/3)

5. Two different sums which are in the ratio 5:4, respectively are invested at 20% p.a. for 4 years and 15% p.a. for 6 years, both at simple interest, respectively. The interest received from the larger sum is Rs. 100 more than that from the smaller sum. Find the amount received when the lesser sum is invested at 25% p.a. simple interest for 3 years.

Correct Answer: (a) Rs. 1750  
Solution:

Let the two sums be Rs. 5x and Rs. 4x respectively.
According to the question,
(5x × 20 × 4)/100 − (4x × 15 × 6)/100 = 100

4x − (18x/5) = 100

x = Rs. 250

Required amount received = (4x × 25 × 3)/100 + 4x
= Rs. 1750

6. Anuradha took a loan of certain amount from a bank at a rate of 20% p.a. compounded annually. She invested 40% of the loan amount in scheme ‘A’ offering simple interest of 32% p.a. and rest in scheme ‘B’ offering compound interest of 15% p.a. compounded annually. If the loss incurred to her at the end of 3 years was Rs. 755.4, then find the simple interest received by her from scheme ‘A’.

Correct Answer: (b) Rs. 9216  
Solution:

Let the amount of loan taken by Anuradha be Rs. 100x

ATQ:
1.20 × 1.20 × 1.20 × 100x − [0.40 × 100x × (1 + 0.32 × 3) + 0.60 × 100x × 1.15 × 1.15 × 1.15] = 755.4

172.8x − [78.4x + 91.2525x] = 755.4

3.1475x = 755.4

x = 240

So, desired amount = 240 × 100 = Rs. 24000

Desired interest = 0.40 × 24000 × 0.32 × 3
= Rs. 9216

7. A certain sum is invested at 15% p.a. simple interest for 3 years. Out of the total amount received, Rs. 1080 is invested in scheme ‘A’ offering simple interest at the rate of 20% p.a. for 4 years while the remaining sum obtained is invested in scheme ‘B’ at the rate of 40% p.a. compound interest, compounded annually for 2 years. If the total interest received from the two schemes together is Rs. 3168, then find the interest received from the original sum.

Correct Answer: (b) Rs. 1080  
Solution:

Let the original sum be Rs. x

Amount received = (x × 15 × 3)/100 + x
= Rs. (29x/20)

According to the question,
{(29x/20) − 1080}(1.4² − 1) = 3168 − (1080 × 20 × 4)/100

(29x/20) − 1080 = 2400

x = 3480 × 20/29 = Rs. 2400

Therefore, interest received
= (2400 × 15 × 3)/100 = Rs. 1080

8. Anant divided Rs. (16A + 8000) in the ratio 3:1:4 and invested them at the rate of simple interest of R%, (R + 4)% and (R + 7)% respectively p.a. The ratio of interest received from the greatest part of money after 3 years to the interest from the lowest part of money after 5 years is 3:1. If the given three sums had been invested for 1 year at respective rates of simple interest then the sum of the interest earned after one year would be Rs. 2400, then find the value of A.

Correct Answer: (a) 750  
Solution:

The greatest part of the money = (16A + 8000) × (4/8)
= Rs. (8A + 4000)

The lowest part of the money = (16A + 8000) × (1/8)
= Rs. (2A + 1000)

Remaining part of the money = (16A + 8000) − [(8A + 4000) + (2A + 1000)]
= Rs. (6A + 3000)

According to the question,
{(8A + 4000) × [(R + 7)% × 3]} : {(2A + 1000) × [(R + 4)% × 5]} = 3 : 1

{4(2A + 1000) × [(R + 7)% × 3]} : {(2A + 1000) × [(R + 4)% × 5]} = 3 : 1

12(R + 7) = 15(R + 4)

12R + 84 = 15R + 60

3R = 24

R = 8

So, the rate of interest = 8%, 12% and 15% respectively.

Again, according to the question,
(6A + 3000) × 8% + (2A + 1000) × 12% + (8A + 4000) × 15% = 2400

0.48A + 240 + 0.24A + 120 + 1.2A + 600 = 2400

1.92A + 960 = 2400

1.92A = 1440

A = 750

Hence, option a.

9. The compound interest received on investing Rs.7,500 for 2 years at ‘y%’ p.a., compounded annually is Rs. 3,663. The simple interest earned on investing Rs. ‘K’ for 2 years at (y + 3)% p.a. is Rs. 184 more than the compound interest received on investing Rs. (K + 400) for 2 years at (y − 2)% p.a., compounded annually. Find the value of ‘K’.

Correct Answer: (c) 6000
Solution:

Compound interest received on investing Rs. 7,500
= Rs. [7500 × {(1 + (y/100))²} − 7500]

So, [7500 × {(1 + (y/100))²} − 7500] = 3663

Or, 7500 × {(100 + y)/100}² = 7500 + 3663

= 11163

Or, {(100 + y)/100}² = 11163/7500 = 1.4884

So, {(100 + y)/100} = √1.4884 = 1.22

So, 100 + y = 122

So, y = 22

Simple interest received on investing Rs. ‘K’ = K × (22 × 3)/100
= Rs. 0.66K

So, compound interest received on investing Rs. (K + 400)
= (K + 400) × {(1 + (20/100))² − 1}
= (K + 400) × 0.44

= Rs. (0.44K + 176)

According to the question,
0.66K = 0.44K + 176 + 184

Or, 0.22K = 360

So, K = 360/0.22 = 6000

Hence, option c.

10. Vikas invested a total sum of Rs. __ in two schemes ‘A’ and ‘B’ such that he invested __ more sum in scheme ‘A’, which offers simple interest at 30% p.a., than in scheme ‘B’, which offers compound interest (compounded annually) of 32% p.a. Total interest earned by him at the end of 2 years from given two schemes together, is Rs. __.

The values given in which of the following options will fill the blanks in the same order in which it is given to make the statement true:

I. 22750, 27.5%, 15090.60
II. 19000, 37.5%, 12539.20
III. 24000, 40%, 15820.50
IV. 27000, 25%, 17908.80

Correct Answer: (c) Only (II) and (IV)
Solution:

For ‘I’:
Sum invested in scheme ‘A’ = {22750 × (127.5/227.5)} = Rs. 12,750

Sum invested in scheme ‘B’ = (22750 − 12750)
= Rs. 10,000

Simple interest earned = {(12750 × 30 × 2)/100} = Rs. 7,650

Compound interest earned = 10000 × [1 + (32/100)]² − 1 = [10000 × (464/625)] = Rs. 7,424

Total interest earned = (7650 + 7424) = Rs. 15,074

So, ‘I’ is false.

For ‘II’:
Sum invested in scheme ‘A’ = {19000 × (137.5/237.5)} = Rs. 11,000

Sum invested in scheme ‘B’ = (19000 − 11000)
= Rs. 8,000

Simple interest earned = {(11000 × 30 × 2)/100} = Rs. 6,600

Compound interest earned = 8000 × [1 + (32/100)]² − 1 = [8000 × (464/625)] = Rs. 5,939.2

Total interest earned = (6600 + 5939.2) = Rs. 12,539.2

So, ‘II’ is true.

For ‘III’:
Sum invested in scheme ‘A’ = {24000 × (140/240)} = Rs. 14,000

Sum invested in scheme ‘B’ = (24000 − 14000)
= Rs. 10,000

Simple interest earned = {(14000 × 30 × 2)/100} = Rs. 8,400

Compound interest earned = 10000 × [1 + (32/100)]² − 1 = [10000 × (464/625)] = Rs. 7,424

Total interest earned = (8400 + 7424)
= Rs. 15,824

So, ‘III’ is false.

For ‘IV’:
Sum invested in scheme ‘A’ = {27000 × (125/225)} = Rs. 15,000

Sum invested in scheme ‘B’ = (22750 − 15000)
= Rs. 12,000

Simple interest earned = {(15000 × 30 × 2)/100} = Rs. 9,000

Compound interest earned = 12000 × [1 + (32/100)]² − 1 = [12000 × (464/625)]
= Rs. 8,908.8

Total interest earned = (9000 + 8908.8)
= Rs. 17,908.8

So, ‘IV’ is true.