BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 1

Total Questions: 60

31. An equal sum is invested for six years in scheme A offering simple interest r % per annum and in scheme B for two years offering compound interest at 10 % per annum (compound annually). The interest earned from scheme A is double the interest earned from scheme B. Had the rate of interest been (r + 2) % simple interest per annum in scheme A, the difference in the interest earned from both the schemes would have been Rs. 8250. What was the sum invested in each of the schemes?

Correct Answer: (e) Rs. 25000
Solution:

Let the sum be Rs. P

Then, For scheme A,
SI = (P × r × 6)/100

For scheme B,
CI = P [(1 + 10/100)² - 1]
= 21P/100

According to the questions,
(P × r × 6)/100 = 2 × 21P/100

or, r = 7%

New rate = (7 + 2) = 9% for SI

Now,
(P × 9 × 6)/100 - 21P/100 = Rs. 8250

33P/100 = Rs. 8250
P = Rs. 25000

Hence, option e.

32. Four years ago, Rakesh had Rs. 10 crore. He purchased a mansion for Rs. 5 crore, a car for Rs. 80 lakh, 12% p.a. (Simple Interest) debentures for Rs. 1.2 crore, gold worth Rs. 2 crore. He placed the remaining money in a bank deposit that pays compound interest @ 8% per annum. If today, he sells off the mansion, the car and the gold at certain percentage of their original value and withdraws his entire money from the bank, the total gain in his assets is 16%. The closest approximate percentage increase in the value of the mansion, the car and the gold viz-a-viz their original value?

Correct Answer: (c) 8%
Solution:

Total amount 4 years ago with Rakesh = Rs. 10,00,00,000 of which bank deposit = Rs. 1,00,00,000

Bank deposit after 4 years @ 8 p.a. CI = Rs. 1,36,04,890

Value of Debentures after 4 years = Amount + Simple Interest = Rs. 1,77,60,000

Total value of assets after 4 years, the total gain in his assets is 16% = Rs. 11,60,00,000

Thus, value of 3 items after 4 years = Rs. 11,60,00,000

(Rs. 1,36,04,890 + Rs. 1,77,60,000) = Rs. 8,46,35,110

The Value of 3 items 4 years ago = Rs. 7,80,00,000

Required %age = (84635110 / 78000000) × 100 ≈ 108.5% i.e. 8%

Hence, option c.

33. A business man invested in 2 types of simple interest bearing securities (S1 and S2). He invested in S1 at the rate of 6% p.a. and 7% p.a. for the S2. After 2 years, he earned Rs 354. One-fourth of the amount invested in S1 is equal to the one-fifth of the amount invested in S2. Calculate the total money the man invested in the securities?

Correct Answer: (b) Rs. 2700 
Solution:

Let the sums be x & y

R1 = 6, R2 = 7, T = 2

(P1 × R1 × T)/100 + (P2 × R2 × T)/100 = 354

(x × 6 × 2)/100 + (y × 7 × 2)/100 = 354

6x + 7y = 17700

Also, x/4 = y/5
5x - 4y = 0
x = 1200
y = 1500
Sum = 1200 + 1500 = 2700
Hence, option b.

34. A part of Rs.77600 is lent at an interest rate of 12% per half year. One year after the first part was lent out, the rest of the amount is also lent at an interest rate of 10% per annum. After 3 years from the time when first part was lent out, the ratio of interest obtained from first part and that from the rest of the amount becomes 5:4 respectively. Find the rest of the amount which was lent at an interest rate of 10% per annum. (Assume simple interest)

Correct Answer: (b) Rs.57,600  
Solution:

Let the first amount lent at an interest rate of 12% per half year = Rs. x and the second amount lent out at an interest rate of 10% per annum = Rs (77600 - x)
Ratio of interest after 3 years from the time when first part was lent out = 5:4

According to question,
=> (24 × 3 × x)/100 : (10 × 2 × (77600 - x))/100
= 5:4

=> (24 × 3 × x)/(10 × 2 × (77600 - x)) = 5/4

=> 72x = 1940000 - 25x
=> 97x = 940000
=> x = Rs. 20000

So, the second part of money that was lent out at an interest rate of 10% per annum = 77600 - 20000 = Rs. 57,600

35. Mr Teja is pursuing his Masters in Security Markets. Eight years after completion of his Master’s degree, he wanted to start a business of his own. To establish his business, he requires to invest Rs. 3,00,000 which is expected to give him a return of 6%, compounded annually. If the expected number of years by which his investment shall double is 72/r, where r is the percent interest rate, the expected total value of investment (in Rs.) his business 60 years later is?

Correct Answer: (a) 9600000  
Solution:

The investment will become double in 72/6 = 12 years.
As the return compounds annually, the amount will be getting doubled in every 12 years.
Therefore, in 60 years, it will become 32 times i.e. 32 × 300000 i.e. 9600000.
Hence, option a.

36. Rs. 1,00,000 was invested by Aamir Khan in fixed deposits with SBI as it gives higher interest rate at 21% per annum at compound interest. However, he has to pay 33.33% penalty on the yearly interest accrued or earned at the end of two years on the maturity of fixed deposit, as he was caught by IT department for using fraudulent measures. How much net interest does Aamir Khan earn after two years?

Correct Answer: (c) Rs. 30940
Solution:

For the first year,
Amount = 100000 × 1.21 = 121000
Interest = 21000

As Amir Khan is paying 33.33% penalty to Income tax department,
Penalty for first year = 21000/3 = 7000

For second year,
Amount = 121000 × 1.21 = 146410
Interest = 121000-146410 = 25410

Penalty for second year = 25410/3 = 8470

Money left with him = 146410 - (7000 + 8470)
= Rs 130940

Therefore, interest earned = 130940 - 100000
= 30940

Hence, option c.

37. Ayush borrowed a sum of money from a friend at 25% compound interest. He was allowed to pay back the money in flexible annual instalments. So, he paid back the money in three years in three different instalments. His instalment at the end of 1st year was Rs. 1000, at the end of 2nd year the instalment was Rs. 1200 and at the end of third year the instalment was Rs. 1125. What the sum of money that he borrowed?

Correct Answer: (c) Rs. 2144
Solution:

Considering the three installments three different loans then

The first installment was full money paid against a sum borrowed for 1 year at 25% C.I.
Principal amount equivalent to 1st year installment = 1000/(1+25/100) = 800

The second installment was full money paid against a sum borrowed for 2 years at 25% C.I.
Principal amount equivalent to 2nd year installment = 1200/[(1+25/100) × (1+25/100)] = 768

The third installment was full money paid against a sum borrowed for 3 years at 25% C.I.

Principal amount equivalent to 3rd year installment
= 1200/(1+25/100) × (1+25/100) × (1+25/100)
= 576

Total Principal amount = 800 + 768 + 576 = 2144
Hence, option c.

38. Mr. Raghunathan invested two different amounts in two different stocks, Stock P and Stock Q. Stock P assures return at 12% simple interest while stock Q assures return at 10% compound interest compound annually. After two years Mr. Raghunathan received Rs.3600 as interest from Stock P. If total amount invested in the two stocks was Rs. 35000, what was the interest received by him from Stock Q after two years?

Correct Answer: (a) Rs. 4200  
Solution:

Let the money invested by Mr. Raghunathan in Stock P be P

Therefore, Money invested in Stock Q = Rs.(35000 - P)

Now, according to the question,
Return received from Stock P = 3600

=> (P × 12 × 2)/100 = 3600
=> P = (3600 × 100)/12 × 2 = Rs.15000

Now, Money invested in Stock Q = Rs.(35000 - 15000) = Rs.20000

Therefore, return received from Company Q
= 20000 × [(1 + (10/100))² - 1]
= 20000 × ((121 - 100)/100)
= Rs.4200

Hence, option a.

39. James and Paul together borrowed Rs. 10,000 from Scarlet. James borrowed the money at 15% simple interest while Paul borrowed the money at 18% simple interest. After 2 years both of them returned the money to scarlet with interest. It was found that the interest returned by James was Rs. 360 more than that of Paul. How much money did James borrow from Scarlet?

Correct Answer: (c) Rs. 6000
Solution:

Let the money lent to James = Rs P

Then, money lent to Paul = Rs (10000 - P) [as total amount = Rs 10000]

SI for amount borrowed by James = (P × 15 × 2)/100
= 3P/10

SI for amount borrowed by Paul = [(10000 - P) × 18 × 2]/100 = 9/25 (10000 - P)

According to the given condition,
(3P/10) - [(9/25)(10000 - P)] = 360

=> (3P/10) - 3600 + 9P/25 = 360
=> 3P/10 + 9P/25 = 360 + 3600
=> 33P/50 = 3960
=> P = 3960 × 50/33
=> P = Rs.6000

Hence, option c.

40. Two persons invested Rs. 25000 each at 8% simple interest for a period of 6 years. At the end of 6 years, one person invested the amount obtained, for a period of 2 years at the rate of 10% compound interest p.a. compounded annually while the other person invested the amount obtained, for a period of 2 years at 12% p.a. simple interest. Find the difference between the compound interest and simple interest earned by the two persons?

Correct Answer: (b) Rs. 1110  
Solution:

Original principal = Rs.25000, rate = 8% and period = 6 years.

Simple Interest = p × n × r/100 = 25000 × 8 × 6/100
= Rs.12000

Hence amount obtained = 25000 + 12000
= Rs.37000

Now for the first person: Principal = Rs.37000, rate = 10% compounded annually and time period = 2 years.

Compound Interest = 37000 × (1 + (10/100))² - 37000
= 37000 × (1.1)² - 37000 = Rs.7770

Now for the second person Principal = Rs.37000, rate = 12% and period = 2 years.

Simple Interest = 37000 × 12 × 2/100 = Rs.8880

Difference in interest earned = 8880 - 7770
= Rs.1110

Hence option b.