BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 2

Total Questions: 60

1. The simple interest calculated on same Principal at rate of interest 25% for 3 years is Rs. ___ and simple interest at 15% per annum for 2 years is Rs. 8400. The difference between interests is Rs. ___.

Correct Answer: (e) 21000, 12600
Solution:

Let Principal = P, Rate = R% per annum, Time = N years

Simple Interest = (P × N × R)/100

Given,
⇒ 8400 = P × 15 × 2/100
⇒ P = 28000

Principal = Rs. 28000

Simple Interest =
= (28000 × 3 × 25)/100
= 21000

Required difference in interest
= 21000 − 8400
= Rs. 12600

2. A lent out Rs. 30000 to B at compound interest at the rate of 20% per annum for 2 years interest is being calculated annually. B lent out the same amount at compound interest at the rate of interest 10% per annum for 2 years calculated annually. What is the profit or loss B had after 2 years?

Correct Answer: (b) Rs. 6900  
Solution:

Given:
A lent out Rs. 30000 to B at compound interest at the rate of 20% per annum for 2 years
B lent out the same amount at compound interest at the rate of interest 10%

Formula Used:
Compound Interest = P(1 + R/100)ⁿ − P
P = principal, R = rate of interest and N = time

Calculation:
Compound Interest = P(1 + R/100)ⁿ − P
P = principal, R = rate of interest and N = time

Then,
Amount A will get after 2 years
= 30000(1 + 20/100)²
= Rs. 43200

Amount B will get after 2 year
= 30000(1 + 10/100)²
= Rs. 36300

B will get Rs. 36300 in a year and he has to return Rs. 43200 to A.

∴ Loss occurred by B = Rs. 43200 − Rs. 36300 = Rs. 6900

3. A sum amounts to Rs. 7776 at 20% p.a. for 2 years if it is compounded annually. If the same sum is invested at 10% p.a. compound interest for the same time period and thrice the sum is invested at 7% p.a. simple interest for 5 years, then find the sum of interest received.

Correct Answer: (e) Rs. 6804
Solution:

Let the amount invested = Rs. P
Amount = Rs. 7776
Rate of interest = 20% p.a.
Time = 2 years

According to question,
7776 = P[(1 + 20%)²]

⇒ P = 7776 / [(1 + 20%)²]
⇒ P = 7776 / (120/100)²
⇒ P = (7776 × 100 × 100)/(120 × 120)

Thus, P = Rs. 5400

Rs. 5400 is invested at 10% p.a. for 2 years at compound interest
So, compound interest = Rs. 1134

Thrice of Rs. 5400 is invested at 7% p.a. for 5 years at simple interest
So, principle = Rs. 16200

Thus, simple interest = Rs. 5670

Sum of interest received = 1134 + 5670 = Rs. 6804

4. Mushkan’s capital is 2/3 times more than Mira’s capital. Mira invested her capital at 40% per annum for 2 years (compounded annually). At what rate of interest per annum at simple interest should Mushkan invest her capital so that after 2 years, they both have the same amount of capital?

Correct Answer: (e) 8.8%
Solution:

Let the capital of Mira = 3

Then Capital of Mushkan = 2/3 times more than Mira

Capital of Mushkan = 2/3 × 3 + 3 = 5

From the given data, we get the below equation.

⇒ Mira’s capital (1 + r/100)²

⇒ 3 (1 + 40/100)² = 5 + [5 × 2 × r/100]

⇒ 3 × 140/100 × 140/100 = 5 + 10r/100

R = 8.8%

5. M lent out Rs 32000 to N at compound interest at the rate of 15% per annum for 2 years, interest being compounded annually. N lent out the same amount at simple interest to O at 20% per annum for 2 years. What will be the loss or profit of N at the end of 2 years?

Correct Answer: (e) None of these
Solution:

Amount M will get from N after 2 years is given by

A = P (1 + R/100)²

⇒ 32000(1 + 15/100)²

⇒ 32000 × 115 × 115/100 × 100

⇒ 16 × 115 × 23

⇒ Rs 42320

Now, SI to be paid by O to N = 32000 × 20 × 2/100

⇒ 320 × 20 × 2
⇒ Rs 12800

∴ Amount N will get after 2 years from O = Rs (32000 + 12800)
⇒ Rs 44800

⇒ N will get Rs 44800 and will pay Rs 42320

So clearly there is profit for N

Profit = Rs (44800 − 42320)
⇒ Rs 2480

∴ Profit for N at the end of 2 years is Rs 2480

6. If the simple interest on Rs. 1200 is Rs. 261 if a person invests ¼ of the amount at the rate 5% for three years. Find the rate at which the remaining amount is invested?

Correct Answer: (d) 8%  
Solution:

Given that 1/4 of 1200 is invested at 5% for three years,

SI = (300 × 3 × 5)/100 ………(1)

Let the remaining amount is invested at x% per annum,

SI = (900 × 3 × x)/100 ………(2)

According to the question,
The Sum of simple interests is Rs. 261

⇒ (1) + (2) = 261

⇒ (300 × 3 × 5)/100 + (900 × 3 × x)/100 = 261

⇒ x = 8%

Hence the rate at which the remaining amount is invested is 8%.

7. A sum of Rs. 8,400 amounts to Rs. 11,046 at 8.75% p.a. simple interest in a certain time. What will be the simple interest (in Rs.) on a sum of Rs. 10,800 at the same rate for the same time?

Correct Answer: (a) 3402  
Solution:

Let S.I for the 1st and 2nd Case be S.I1 and S.I2

Now, According to the question
S.I1 = 11046 − 8400 = 2646

So, According to the formula used
(8400 × 8.75 × T)/100 = 2646

⇒ 73500T = 264600

⇒ T = 3.6 years

Now, We have to find S.I2

So, S.I2 = (10800 × 8.75 × 3.6)/100

⇒ S.I2 = 3402

∴ The simple interest for the 2nd case is Rs. 3402

8. Lata borrows a certain sum of money from a money lender at the rate of 25% per annum, interest being compounder annually. She agrees to return it in two equal yearly installment of Rs 800 each. Find the sum borrowed.

Correct Answer: (a) Rs. 1152  
Solution:

Present value of Rs 800, which will be due at the end of 1st year = Rs 800/(1 + 25/100)
⇒ Rs 800/(125/100) = Rs 800 × 20/25 = Rs 640

Now, present value of Rs 800, which will be due at the end of 2nd year = Rs 800/(1 + 25/100)²
⇒ Rs 800/(125/100)²
⇒ Rs (800 × 20 × 20)/25 × 25 = Rs 512

∴ Total principal = Rs (640 + 512) = Rs 1152
∴ The sum borrowed is Rs 1152

9. The difference between simple interest and compound interest on a certain amount of money for 2 years is Rs. 4.20. The rate of interest per annum is 5% (both S.I. and C.I). Find the sum of money.

Correct Answer:   (b) Rs. 1680  
Solution:

Let, the sum be p
Here, T = 2 years, R = 5%

So, S.I = (P × 5 × 2)/100 = (P/10)

Again, n = 2 years, r = 5%

So, C.I = P[(1 + (5/100))² − 1]
⇒ C.I = P[(1 + (1/20))² − 1]
⇒ C.I = P[(441/400) − 1]
⇒ C.I = P[41/400]

Now, according to the question, we can say,
P[41/400] − (P/10) = 4.2
⇒ P[(41/400) − (1/10)] = 4.2
⇒ P[(41 − 40)/400] = 4.2
⇒ P[1/400] = 4.2
⇒ P = 4.2 × 400 = 1680

∴ The sum of money is Rs. 1680

10. A man wants to invest Rs. 40,440 in bank account of his two sons whose age were 12 years and 16 years in such a way they will get equal amount at age of 20 years @ 33⅓% per annum compounded annually. Find the share of younger son?

Correct Answer: (b) Rs. 9720  
Solution:

Let the principal for younger son be Rs x
Principal for elder son be Rs y

Interest to be calculated for
Younger son = (20 − 12) = 8 years
Elder son = (20 − 16) = 4 years

Since, amount will be equally distributed then,
⇒ x (1 + 100/300)⁸ = y (1 + 100/300)⁴
⇒ x (4/3)⁸ = y (4/3)⁴

⇒ (4/3)^(8−4) = y/x
⇒ y/x = 256/81

∴ Younger son’s share = 81/337 × 40,440 = Rs. 9,720