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## Arithmetic: Compound Interest Test -2

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Question 1 |

Find the total amount due when Rs. 2000 is compounded annually at the rate of 5% three years.

A | 2305 |

B | 2315 |

C | 2405 |

D | 2505 |

Question 1 Explanation:

Given values

Principal=2000

Rate = 5%

Time =3 years

So the amount can be calculated using the formula:

A = P (1+R/100)

A = 2000(1+5/100)

A = 2000(1+1/20)

A = 2000 x 21/20 x 21/20 x 21/20 =Rs. 2315.25

Hence, option b is the right answe

Principal=2000

Rate = 5%

Time =3 years

So the amount can be calculated using the formula:

A = P (1+R/100)

^{t}A = 2000(1+5/100)

^{3}A = 2000(1+1/20)

^{3}A = 2000 x 21/20 x 21/20 x 21/20 =Rs. 2315.25

Hence, option b is the right answe

Question 2 |

Meera got a Rs 4000 loan from Richa for a time period of 2 years 2 months and at a rate of 2% per annum. Find the amount paid by Meera to Richa as compound Interest.

A | 4175 |

B | 175 |

C | 156 |

D | 4235 |

Question 2 Explanation:

Since we have to find the compound interest

We have the formula for amount when time given is in fractions is

A = P (1+R/100)

So the amount is = 4000(1+2/100)

= 4000(1+1/50)

= 4000 x( 51/50 x 51/50){301/300}

A = Rs 4175.30

Compound Interest= 4175 – 4000 = Rs 175

We have the formula for amount when time given is in fractions is

A = P (1+R/100)

^{y}{1+ (m/12 X R/100)} where y is the number of years and m is the monthsSo the amount is = 4000(1+2/100)

^{2}{1+ (2/12 X 2/100)}= 4000(1+1/50)

^{2}{1+ (1/6 X 1/50)}= 4000 x( 51/50 x 51/50){301/300}

A = Rs 4175.30

Compound Interest= 4175 – 4000 = Rs 175

Question 3 |

An amount of 7500 is invested in a compound interest scheme for 4 years. The rate of interest is 2% for the first year, 3 % for next 2 years, and for the last year, it is 4%. The final amount is:

A | 8356.7 |

B | 8557.45 |

C | 8440 |

D | none |

Question 3 Explanation:

It is a logical question

Given values are

Principal = 7500

Rate = 2%, 3%, 4%

Time 4 years

Since the rate is varying with respect to time so

Amount for first year

A =P(1+R/100)

A = 7500(1+2/100) =Rs.7650

Therefore, this amount acts as the principal for the next two years and the

rate for the next two years the rate is 3%, the amount will be

A = 7650(1+3/100)

For the fourth year, the amount above acts as the principal.

The rate of interest for the last year is 4%, therefore the final amount becomes:

A=8115(1+4/100) = 8440

Given values are

Principal = 7500

Rate = 2%, 3%, 4%

Time 4 years

Since the rate is varying with respect to time so

Amount for first year

A =P(1+R/100)

A = 7500(1+2/100) =Rs.7650

Therefore, this amount acts as the principal for the next two years and the

rate for the next two years the rate is 3%, the amount will be

A = 7650(1+3/100)

^{2}= 8115.885For the fourth year, the amount above acts as the principal.

The rate of interest for the last year is 4%, therefore the final amount becomes:

A=8115(1+4/100) = 8440

Question 4 |

The amount that a person would receive when he invest Rs.5600 at 4% rate for 1 year, compounded half yearly, is:

A | 5789 |

B | 5956 |

C | 5826 |

D | 6897 |

Question 4 Explanation:

For half yearly compounding, the formula is:

A = P {(1+R/2)/ 100}

A = 5600{(1+4/100)

A = 5600 x 51/50 x 51/50 =5826.24=Rs. 5826

A = P {(1+R/2)/ 100}

^{2T}A = 5600{(1+4/100)

^{2}A = 5600 x 51/50 x 51/50 =5826.24=Rs. 5826

Question 5 |

Find the compound interest on Rs. 4500 at 16% rate for 6 months compounded quarterly.

A | 366.4 |

B | 364.5 |

C | 325.7 |

D | 367.2 |

Question 5 Explanation:

For quarterly compound interest, the formula is:

A = P {(1+R/4)/ 100}

A = 4500{(1+16/4) /100}

A = 4500{(1+4/100}

A = 4500{(1+1/25)}

A = 4500 x 26/25 x 26/25=Rs 4867.2

So the compound interest will be 4867.2 – 4000 = Rs 367.2

A = P {(1+R/4)/ 100}

^{4T}A = 4500{(1+16/4) /100}

^{4x6/12}A = 4500{(1+4/100}

^{2}A = 4500{(1+1/25)}

^{2}A = 4500 x 26/25 x 26/25=Rs 4867.2

So the compound interest will be 4867.2 – 4000 = Rs 367.2

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