Important for :

1

B

P = 4800, T = 3 years, R = 5%By the net% effect we would calculate the effective compound rate of interest for 3 years = 15.76% (Refer to sub-details)

Therefore, CI = 15.76% of 4800

CI = | 15.76 × 4800 | = ₹ 756.5 |

100 |

Calculation of effective compound rate of interest for 3 years will be as follows.

For the first 2 years, let's apply the net% effect.

Here, x = y = 5%

Net% effect = x + y = | xy | |

100 |

= 5 + 5 + | 5 × 5 | = 10 + 0.25 = 10.25% |

100 |

Now let's take this 10.25% as x and 5% as y for the calculation of 3rd year.

= 10.25 + 5 + | 10.25 × 5 | = 15.25 + .51 = 15.76% |

100 |

________________________________________________

CI = 4800 | [( | 1 + | 5 | ) |
^{3} |
– 1 | ] |

100 |

= 4800 | [ | 21 × 21 × 21 – 20 × 20 × 20 | ] |

20 × 20 × 20 |

= 4800 × | ( | 9261 – 8000 | ) | ⇒ 4800 × | 1261 | = ₹ 756.6. |

20 × 20 × 20 | 8000 |

Hence, option B is correct.

2

A

To solve this question, we can apply a short trick approach

Sum = |
Difference × 100^{2} |

r^{2} |

Given,

Sum (Amount) = 15000, Difference = 96, r = ?

By the short trick approach, we get

15000 = |
96 × 100^{2} |
⇒ r^{2} = |
96 × 100^{2} |
⇒ r^{2} = 64 ⇒ r = 8% |

r^{2} |
15000 |

As per the information, we get the eqn.

CI for 2 years – SI for 2 years = 96

[ | 15000 × | ( | 1 + | R | ) |
^{2} |
– 15000 | ] | – | ( | 15000 × R × 2 | ) | = 96 |

100 | 100 |

⇒ 15000 | [( | 1 + | R | ) |
^{2} |
– 1 – | 2R | ] | = 96 |

100 | 100 |

⇒ 15000 | [ |
(100 + R^{2}) – 10000 – 200 R |
] | = 96 |

10000 |

⇒ R^{2} = |
96 × 2 | = 64 ⇒ R = 8. |

3 |

Hence, option A is correct.

3

C

Since increase in interest in 6 years = 60%Therefore, increase in interest in 1 year = 10% (Rate of interest)

Now, P = 12000, T = 3 years & R = 10% p.a.

By the net% effect we would calculate the effective compound rate of interest for 3 years = 33.1% (Refer to sub-details)

Therefore, CI = 33.1% of 12000

CI = | 33.1 × 12000 | = ₹ 3972. |

100 |

Calculation of effective compound rate of interest for 3 years will be as follows.

For the first two years, let's apply the net% effect.

Here, x = y = 10%

Net% effect = x + y = | xy | |

100 |

= 10 + 10 + | 10 × 10 | = 21% |

100 |

Now let's take this 21% as x and 10% as y for the calculation of 3rd year.

= 21 + 10 + | 21 × 10 | = 33.1% |

100 |

Hence, option C is correct.

4

A

Yearly rate of interest = 10%Rate of interest charged on half yearly basis = 5%

It's given that the financier charges interest on half yearly basis. Hence, he actually charges Compound Interst and not Simple Interest.

Therefore, applying the net% effect formula for effective rate of compound interest for 2 half years (1 year = 2 half years), we get

Net% effect = x + y + | xy | |

100 |

x = y = 5%

Net% effect = 5 + 5 + | 5 × 5 | = 10 + 0.25 = 10.25% |

100 |

Hence, option A is correct.

5

A

To solve this question, we can apply a net% effect formula
Net% effect = x + y + |
xy |
% |

100 |

x = y = 10%

= 10 + 10 + | 10 × 10 | = 21% |

100 |

Now, Amount (P + CI) = (100 + 21)% = 121% | ≡ | ₹ 12100 |

∴ Principal = 100% |
≡ | ₹ x |

By the cross multiplication, we get

x = | 12100 × 100 | = ₹ 10000. |

121 |

__________________________________________________________

Given,

Amount = 12,100; r = 10%, t = 2 yrs

Amount = | P | [ | 1 + | r | ] |
^{t} |

100 |

12100 = | P | [ | 1 + | 10 | ] |
^{2} |

100 |

⇒ 12100 = | P | [ | 11 | ] |
^{2} |
⇒ 12100 = P × | 11 | × | 11 |

10 | 10 | 10 |

⇒ P = ₹ 10,000.

Hence, option A is correct.