BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 1

Total Questions: 60

11. A sum of money at compound interest doubles itself in 4 years. In how many years will it be 32 times itself? [(e) 32 years]

Correct Answer: (d) 20 years  
Solution:Let the sum of money be Rs. P, rate of interest be r% p.a.
Therefore,
2P = P(1+r/100)⁴
Similarly
4P = P(1+r/100)⁴(1+r/100)⁴
i.e. in 8 years it becomes 4 times
Similarly
12 yrs = 8 times
16 yrs = 16 times
20 yrs = 32 times
Hence, option d

12. The difference between simple and compound interest on a sum of money for 2 years at 13% per annum is Rs. 169. The sum is?

Correct Answer: (d) Rs. 10000  
Solution:

CI - SI = 169
{P(1 + R/100)ᵀ - P} - {(P × R × T)/100} = 169
[P(1 + R/100)² - P] - [(P × R × 2)/100] = 169
P{1 + (R/100)² + 2R/100 - 1 - 2R/100} = 169
P × (R/100)² = 169
P × (13/100)² = 169
P = (169 × 100 × 100)/(13 × 13)
P = 10000

13. Ghanshyam buys a second hand car for Rs. 70000. The value of the car depreciates at a rate of R% every year. If the car was sold at a price of Rs. 47068 after two years then, find the value of R.

Correct Answer: (c) 18%
Solution:According to question,
so, 70000 × (1 - R/100)² = 47068
(1 - R/100)² = 47068/70000
(1 - R/100) = 82/100
R/100 = 1 - 82/100
Therefore, R = 18%
Hence, option c.

14. Surbhi lent a certain amount of money at 8% simple interest and after 10 years she received an interest amount of Rs. 560 less than the amount she had lent. How much money did she lend?

Correct Answer: (c) Rs. 2800
Solution:Let, the amount Surbhi had lent be Rs. x
So, interest = (x × 8 × 10)/100
According to question,
x - (x × 8 × 10)/100 = 560
100x - 80x = 56000
20x = 56000
x = 2800
Therefore, the amount Surbhi had lent = Rs. 2800
Hence, option c

15. A sum of Rs. 10,000 is lent at compound interest of 10% per annum. If the amount is lent for two years then what will be the interest amount in 2nd year?

Correct Answer: (c) Rs.1100
Solution:

Total interest of 2 years = 10,000 × ((1 + 1/10)² - 1)
= Rs. 2,100
Interest of first year = 10,000 × ((1 + 1/10) - 1)
= Rs. 1,000
Therefore, interest amount of 2nd year = 2,100 - 1,000 = Rs. 1100
Hence, option c.

16. Nirmal takes a sum of Rs. 1,55,000 as a loan. He has to repay this in two equal annual instalments. If the rate of interest be 20% compounded annually, the value of each instalment is-

Correct Answer: (d) Rs. 1,01,455
Solution:

Let, the value of each instalment be x.

Then,
x/(1 + 20/100) + x/(1 + 20/100)² = 155000

Or,
x/(120/100) + x/(144/100) = 155000

Or,
x × 100/120 + x × 100/144 = 155000

Or,
5x/6 + 25x/36 = 155000

Or,
(30x + 25x)/36 = 155000

Or,
55x = 155000 × 36

Or,
x = 101455. Hence, option d.

17. A sum of money invested for a certain number of years at 9% p.a. simple interest grows to Rs.190. The same sum of money invested for the same number of years at 4.5% p.a. simple interest grows to Rs.100. For how many years was the sum invested?

Correct Answer: (a) 200 years  
Solution:

From the information provided, we know that,
Principal + 9% p.a. interest on principal for n years = 190 ……… (1)
Principal + 4.5% p.a. interest on principal for n years = 100 ……… (2)

Subtracting equation (2) from equation (1), we get
4.5% p.a. interest on principal for n years = Rs. 90.

Now, we can substitute this value in equation (2),
i.e. Principal + 90 = 100
= Principal = Rs.10.

We know that SI = pnr/100, where p is the principal, n the number of years and r the rate percent of interest.

In equation (2), p = Rs.10, r = 4.5% p.a. and the simple interest = Rs.90.
Therefore, 90 = (10 × n × 4.5)/100
=> n = 100 × 2 = 200 years. Hence, option a.

18. Shokie and Shanty have equal amounts. Shokie invested his entire amount at 10% compounded annually for 2 years and Shanty invested ¼ at 10% compound interest (annually) and rest at r% per annum at simple interest for the same 2 years period. The amount received by both at the end of 2 years is same. What is the value of r?

Correct Answer: (c) 10.5%
Solution:

Let the amount of investment with each one be Rs. 4000, then
entire amount at 10% compounded annually for 2 years = 4000(1.1)²
1/4th amount at 10% compound interest (annually) for 2 years = 1000(1.1)²
rest of the amount at r% per annum at simple interest for the same 2 years period = [3000 + (3000 × r × 2)/100]

4000 (1.1)² = 1000 (1.1)² + [3000 + (3000 × r × 2)/100]
r = 10.5%
Hence, option c.

19. A sum of money becomes 11/6 of itself in 5 years at a certain rate of interest on simple interest. How much will Rs 3000 amount to at the same rate of interest in 2 years on simple interest?

Correct Answer: (d) Rs 4000  
Solution:

Let the sum of money be x. Amount in 5 years = 11x/6. Interest = 11x/6 - x = 5x/6
500x = (x × r × 5 × 6) => r = 50/3%
Required amount = 3000 + (3000 × 50/3 × 2)/100
= 4000
Hence, option d.

20. A sum of money amounts to Rs. 220 after a year at 10% per annum compound interest. What will be the amount if ten times the money invested in the above scheme is invested in another scheme for two years where the interest is compounded annually, but the rate in this scheme is half of the rate of previous scheme?

Correct Answer: (c) Rs. 2205
Solution:

Let the amount of money invested in the first scheme (providing simple interest) = P.
220 = P(1 + 10/100) => P = 200

In the second scheme (providing compound interest), amount invested = Rs. 2000.
Total amount after two years at the rate of 5% per year =
2000 × (1 + 5/100)² = Rs. 2205
Hence, option c.