Important for :

1

B

Time = 2 years 4 months = 2 | 4 | years = 2 | 1 | years. |

12 | 3 |

Let principal = P, Rate = R% per annum, Time = n years.

When interest is compounded annually. then,

Amount = P | ( | 1 + | R | ) |
^{n} |

100 |

So, amount = Rs | [ | 7000 × | ( | 1 + | 21 | ) |
^{2} |
] | × | ( | 1 + | 1/3 × 21 | )] |

100 | 100 |

⇒ Rs. | ( | 7000 × | 121 | × | 121 | × | 107 | ) |

100 | 100 | 100 |

⇒ 10966.1.

So, C.I. = Rs. (10966.1 – 7000) ⇒ Rs. 3966.1.

Hence, option B is correct.

2

A

When interest is compounded Half-yearly. then,Amount = P | [ | 1 + | (R/2) | ] |
^{2T} |

100 |

Principal = Rs. 7500; Rate = 3% per half - year; Time = 2 years = 4 half - years.

So, Amount = Rs. | [ | 7500 × | ( | 1 + | 3 | ) | 4 | ] |

100 |

⇒ Rs. | ( | 7500 × | 103 | × | 103 | × | 103 | × | 103 | ) |

100 | 100 | 100 | 100 |

⇒ Rs. 8441.31

⇒ C.I = Rs. (8441.31 - 7500) = Rs. 941.31.

Hence, option A is correct.

3

C

P = 10000, T = 6 months, R = 20/4 = 5% (rate of interest apply quaterly)By the net% effect we would calculate the effective compound rate of interest for 6 months = 10.25%

CI = 10.25% of 10000

CI = | 10.25 × 10000 | = 1025. |

100 |

Calculation of effective compound rate of interest for 2 quaters (6 months) will be as follows.

Here, x = 5 and y = 5%

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

100 |

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

100 |

_______________________________________________________

When interest is compounded Quarterly. then,

Amount = P | [ | 1 + | (R/4) | ] |
^{4T} |

100 |

Principal = Rs. 10000; Time = 6 months = 2 quarters; Rate = 20% per annum = 5% per quarter

So, Amount = Rs | [ | 10000 × | ( | 1 + | 5 | ) | 2 | ] |

100 |

⇒ Rs | ( | 10000 × | 21 | × | 21 | ) | ⇒ 11025. |

20 | 20 |

So, C.I = Rs (11025 – 10000) ⇒ Rs 1025.

Hence, option C is correct.

4

B

We know, thatSI = rt% (rate of interest & time) and by the net% effect we would calculate the effective compound rate of interest for 2 years = 10.25%

1400 = (2 × 5)%

So, 10% ≡ ₹ 1400

10.25% ≡ ₹ x

By the cross multiplication, we get

x = | 1400 × 10.25 | = ₹ 1435. |

10 |

Sub-details:

Calculation of effective compound rate of interest for 2 years will be as follows.

Here, x = 5 and y = 5%

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

100 |

= 5 + 5 + | 5 × 5 | = 10 + .25 = 10.25% |

100 |

_______________________________________________________________________

Clearly, Rate = 5% p.a, Time = 2 years, S.I = Rs. 1400.

So, principal = Rs. | ( | 100 × 1400 | ) | = Rs. 14000. |

2 × 5 |

Amount = Rs. | [ | 14000 × | ( | 1 + | 5 | ) |
^{2} |
] | ⇔ Rs. | ( | 14000 × | 21 | × | 21 | ) | ⇒ Rs. 15435. |

100 | 20 | 20 |

So, C.I = Rs. (15435 – 14000) = Rs. 1435.

Hence, option B is correct.

5