BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 2

Total Questions: 60

11. The difference between compound interest and simple interest on a sum for 2 years at 8% per annum when the interest is compounded annually is Rs.16. If the interest were compounded half yearly, the difference between the two interests would be?

Correct Answer: (b) Rs 24.64  
Solution:

From the formula
P (8/100)² = 16
P = Rs 2500

Now, In second case interest compounds on half yearly basis. So Rate of interest = 8/2 = 4%
Time = 2 × 2 = 4 years

Now, S.I = PRT/100
S.I = (2500 × 4 × 4)/100 = 400

C.I = P × (1 + R/100)ᵗ − P
C.I = 2500 × (1 + 4/100)⁴ − 2500
= 2500 × (1 + 4/100)⁴ − 2500 = 2,924.6464 − 2500
= 424.6464

Difference = CI − SI = 424.64 − 400 = Rs. 24.64

12. Ratio of CI earned only for 3rd year to CI earned only for 2nd year on an amount Rs. X at R% per annum is 11/10 and CI earned on Rs. (X + 1500) in 2 years at the same rate is Rs. 1890. Find the value of X.

Correct Answer: (b) Rs. 7500  
Solution:

According to question,

x[(1 + R/100)³ − x(1 + R/100)²] / [x(1 + R/100)² − x(1 + R/100)] = 11/10

⇒ 1 + R/100 = 11/10

⇒ R = 10%

Now,

(x + 1500) (1 + 10/100)² − (x + 1500) = 1890

⇒ (x + 1500) [(121/100) − 1] = 1890

⇒ (x + 1500) (21/100) = 1890

⇒ (x + 1500) = 1890 × 100/21

⇒ (x + 1500) = 9000

∴ x = 9000 − 1500 = Rs 7500

13. If the difference between C.I and S.I on a certain sum of money at the rate of 15% per annum for two years is Rs. 405, then find the sum.

Correct Answer: (a) Rs. 18,000  
Solution:

So, 405 = P (15/100)²

⇒ 405 = P × 9/400

⇒ P = (405 × 400)/9

⇒ P = 45 × 400 = Rs. 18,000

Therefore the correct answer is Rs. 18000

14. Prashant invested Rs. 25,000 for 2 years in bank A which offers 20% p.a. compound interest compounded annually. He also invested the same amount of money in bank B for the same time at certain rate of simple interest. Interest received by him from bank A is twice of that received from bank B. Find the rate of interest offered by bank B?

Correct Answer: (b) 11%  
Solution:

Let the rate of interest offered by bank B = r% p.a.

25000[(1 + 20/100)² − 1] = 2 × 25000 × r × 2/100

⇒ 11/25 = r/25

⇒ r = 11%

15. Aron is the father of Abel, Abraham, and Adam whose age is 13, 7, and 5 years respectively. Aron wants to distribute his Rs. 1,58,000 in such a way that when their children get married at the age of 25 years. They should get equal simple interest. If he invested capital at 12%, 6%, and 24% rate of interest. Find out the money share of the youngest one.

Correct Answer: (b) Rs. 18000  
Solution:

Let, Rs. 1,58,000 be distributed in P1 : P2 : P3

Their simple interest on the sum are the same for all.

Time-Period for them = (25 − 13 = 12) years, (25 − 7 = 18) years, (25 − 5 = 20) years

⇒ I1 = I2 = I3

⇒ P1R1N1 = P2R2N2 = P3R3N3

⇒ P1 × 12 = P2 × 6 × 18 = P3 × 24 × 20

⇒ P1 × 12 = P2 × 9 = P3 × 40

⇒ L.C.M. of 12, 9, 40 is 360

⇒ P1 = 30, P2 = 40, P3 = 9

⇒ P1 : P2 : P3 = 30 : 40 : 9

∴ Divide Rs. 1,58,000 in 30 : 40 : 9

⇒ P1 = 158000 × 30/79 = 60000
⇒ P2 = 158000 × 40/79 = 80000
⇒ P3 = 158000 × 9/79 = 18000

∴ The youngest one will get Rs. 18000

16. A person invested in 2 schemes one at 10% per annum and another at 20% per annum. After 3 years, he gained Rs. 5400 as simple interest from both the schemes. He invested a total of Rs. 12000. Find the share of investment in each scheme.

Correct Answer: (b) Rs. 6000, Rs. 6000
Solution:

Simple Interest = (Principal × Rate × time)/100

⇒ 5400 = (12000 × Rate × 3)/100

⇒ Rate = 15%

By the rule of mixture and allegation

1st Scheme — 10%
2nd Scheme — 20%

Mean = 15%

20 − 15 = 5
15 − 10 = 5

Ratio of principal = 1 : 1

Total principal = Rs. 12000

⇒ 2 units = Rs. 12000
⇒ 1 unit = Rs. 6000

∴ Person invested in each scheme = Rs. 6000

17. A person borrowed a sum of Rs. 16000 at the rate of interest 15% per annum for 1 year. Find the compound interest if the interest is calculated every 4 months.

Correct Answer: (b) Rs. 2522 
Solution:

Rate of interest (when interest calculated every 4 month) = 15%/3 = 5%

t = 1 year / 4 month = 12/4 = 3

Amount = 16000 × (1 + 5/100)³

⇒ A = 16000 × (21/20)³

⇒ A = 18522

Amount = 16000 + Compound Interest

⇒ 18522 = 16000 + Compound Interest

⇒ Compounded Interest = Rs. 2522
∴ The interest paid by the person = Rs. 2522

18. A person invested a certain sum of money at certain rate of simple interest for 2 years. After 2 years, he gets Rs. 800 as simple interest. Had he invested same sum in another scheme at same rate of compound interest for 2 years he would have got Rs. 840 as interest. Find the sum.

Correct Answer: (b) Rs. 4000  
Solution:

Simple interest = (x × y × 2)/100
⇒ 800 = xy/50
⇒ 40000 = xy
⇒ 40000/x = y ……(i)

From 2nd condition
Amount = x × (1 + y/100)²
⇒ 840 + x = x × (1 + y/100)² [Amount = Principal + C.I]

⇒ 840 + x = x × (1 + 40000/100x)²
⇒ 840 + x = x × [(x + 400)²/x²]
⇒ (840 + x) × x = x² + 800x + 160000
⇒ 40x = 160000
⇒ x = Rs. 4000

∴ The sum invested by person = Rs. 4000

19. Mohan invested Rs. 5000 at x% simple interest for 2 years. After 2 years, he noticed that if he has given the money on compound interest then he would have got Rs. 72 more as interest. Find the rate of interest?

Correct Answer: (c) 12%
Solution:

Simple Interest = (5000 × x × 2)/100
Simple interest = 100x

Amount = 5000 × (1 + x/100)²
⇒ Principal + C.I = 5000 × {(100 + x)/100}²

⇒ C.I = (x² + 200x − 10000)/2 − 5000
⇒ C.I = x²/2 + 100x

According to question,
C.I − S.I = Rs. 72
⇒ x²/2 + 100x − 100x = 72
⇒ x²/2 = 72
⇒ x = 12

∴ Rate of Interest = 12%

20. Find the difference, between difference of C.I. and S.I. for 3 years and the difference of C.I and S.I for 2 years if Principal is 2000 and rate is 10% per annum.

Correct Answer: (a) 42  
Solution:

For 3 years,
C.I − S.I = P (r/100)² (300 + r)/100

= 2000 × (10/100)² (300 + 10)/100
= 2000 × (10/100)² × 310/100
= 62

For 2 years,
C.I − S.I = P (r/100)²
= 2000 × (10/100)²
= 20

∴ It is asking the difference, between Difference of C.I and S.I of 3 and 2 years so required difference = 62 − 20 = 42