Simple Interest Questions and Answers

Q: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?

\[ \text{SI} = \frac{P \times R \times T}{100} \]The three years between the two amounts give the yearly interest.\[ \frac{12005 - 9800}{3} = \frac{2205}{3} = \text{Rs. } 735 \text{ per year} \]\[ P = 9800 - 5 \times 735 = 9800 - 3675 = \text{Rs. } 6125 \]\[ R = \frac{735 \times 100}{6125} = 12\% \]

Q: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Equal interests over the same period give\[ \frac{p_{1} \times 9 \times T}{100} = \frac{p_{2} \times 12 \times T}{100} \]\[ 9\,p_{1} = 12\,p_{2} \quad\Longrightarrow\quad \frac{p_{1}}{p_{2}} = \frac{12}{9} = \frac{4}{3} \]The sums are in the inverse ratio of the rates: the lower rate needs the larger capital to earn as much.

Q: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Two years and six months is 2.5 years.\[ \text{SI} = \frac{8200 \times 17.5 \times 2.5}{100} \]\[ = 82 \times 17.5 \times 2.5 = 82 \times 43.75 = \text{Rs. } 3587.50 \]The six months must be converted to 0.5 of a year, not left as a separate term.

Q: In what time a sum of money double itself at 3% per annum simple interest?

\[ \text{SI} = \frac{P \times R \times T}{100} \]Doubling means the interest equals the principal.\[ P = \frac{P \times 3 \times T}{100} \quad\Longrightarrow\quad 100 = 3T \]\[ T = \frac{100}{3} = 33\tfrac{1}{3} \text{ years} \]The rule is simply \( T = \tfrac{100}{R} \) for doubling under simple interest.

Q: At what rate per cent per annum will the simple interest on a sum of money be \( \dfrac{2}{5} \) of the sum in 10 years?

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \frac{2}{5}P = \frac{P \times R \times 10}{100} \]The \( P \) cancels:\[ \frac{2}{5} = \frac{10R}{100} = \frac{R}{10} \quad\Longrightarrow\quad R = 4\% \]Checking: 4% for 10 years gives 40% of the sum, which is \( \tfrac{2}{5} \).

Q: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?

\[ \text{SI} = \frac{P \times R \times T}{100} \]The extra income comes from the \( 12\tfrac{1}{2} - 10 = 2.5 \) percentage points, over one year.\[ \frac{P \times 2.5 \times 1}{100} = 1250 \]\[ 0.025P = 1250 \quad\Longrightarrow\quad P = \text{Rs. } 50{,}000 \]Checking: Rs. 5000 a year at 10% against Rs. 6250 at 12.5%.

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71.

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?

A.5%
B.8%
C.12%
D.15%

Answer: C

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The three years between the two amounts give the yearly interest.

\[ \frac{12005 - 9800}{3} = \frac{2205}{3} = \text{Rs. } 735 \text{ per year} \]

\[ P = 9800 - 5 \times 735 = 9800 - 3675 = \text{Rs. } 6125 \]

\[ R = \frac{735 \times 100}{6125} = 12\% \]

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72.

A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?

A.2:3
B.3:4
C.4:3
D.None

Answer: C

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Equal interests over the same period give

\[ \frac{p_{1} \times 9 \times T}{100} = \frac{p_{2} \times 12 \times T}{100} \]

\[ 9\,p_{1} = 12\,p_{2} \quad\Longrightarrow\quad \frac{p_{1}}{p_{2}} = \frac{12}{9} = \frac{4}{3} \]

The sums are in the inverse ratio of the rates: the lower rate needs the larger capital to earn as much.

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73.

How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?

A.Rs. 3770
B.Rs. 2850.50
C.Rs. 3587.50
D.Rs. 3750

Answer: C

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Two years and six months is 2.5 years.

\[ \text{SI} = \frac{8200 \times 17.5 \times 2.5}{100} \]

\[ = 82 \times 17.5 \times 2.5 = 82 \times 43.75 = \text{Rs. } 3587.50 \]

The six months must be converted to 0.5 of a year, not left as a separate term.

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74.

The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?

A.Rs.800
B.Rs.900
C.Rs.1200
D.Rs.1500

Answer: C

Rs. 600 over ten years means Rs. 60 a year on the original principal.

First five years at the original principal:

\[ 5 \times 60 = \text{Rs. } 300 \]

Next five years with the principal trebled, so three times the yearly interest:

\[ 5 \times 180 = \text{Rs. } 900 \]

\[ \text{total} = 300 + 900 = \text{Rs. } 1200 \]

Trebling the whole Rs. 600 would give Rs. 1800; only the second half of the period is affected.

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75.

Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?

A.Rs. 20,000
B.Rs. 22,000
C.Rs. 24,000
D.Rs. 25,000

Answer: A

Let the second amount be Rs. x. Then,

(12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100

120000 + 20x = 16800 + 14x

x = 8000

Total investment = 12000 + 8000 = Rs. 20,000.

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76.

In what time a sum of money double itself at 3% per annum simple interest?

A.29 years
B.33 1/3 years
C.23 1/3 years
D.13 1/3 years

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Doubling means the interest equals the principal.

\[ P = \frac{P \times 3 \times T}{100} \quad\Longrightarrow\quad 100 = 3T \]

\[ T = \frac{100}{3} = 33\tfrac{1}{3} \text{ years} \]

The rule is simply \( T = \tfrac{100}{R} \) for doubling under simple interest.

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77.

At what rate per cent per annum will the simple interest on a sum of money be \( \dfrac{2}{5} \) of the sum in 10 years?

A.4%
B.5 2/3 %
C.6%
D.6 2/3 %

Answer: A

\[ \text{SI} = \frac{P \times R \times T}{100} \]

\[ \frac{2}{5}P = \frac{P \times R \times 10}{100} \]

The \( P \) cancels:

\[ \frac{2}{5} = \frac{10R}{100} = \frac{R}{10} \quad\Longrightarrow\quad R = 4\% \]

Checking: 4% for 10 years gives 40% of the sum, which is \( \tfrac{2}{5} \).

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78.

If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?

A.45000
B.50000
C.60000
D.65000

Answer: B

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The extra income comes from the \( 12\tfrac{1}{2} - 10 = 2.5 \) percentage points, over one year.

\[ \frac{P \times 2.5 \times 1}{100} = 1250 \]

\[ 0.025P = 1250 \quad\Longrightarrow\quad P = \text{Rs. } 50{,}000 \]

Checking: Rs. 5000 a year at 10% against Rs. 6250 at 12.5%.

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79.

What time will be taken by an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A.2 years
B.1 years
C.3 years
D.4 years

Answer: A

P= Rs 900

Rate = 4.5*

SI= Rs 81

=> SI= Time*P*rate

calculating for rate,

=> Time= SI/rate*P

= 81/4.5%*900

=> 2 years

Thus, it will take 2 years to yield Rs 81.

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80.

A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 840 in the same period of 2 years, what must be the rate of interest?

A.5% p.a.
B.7.5% p.a.
C.10% p.a.
D.12.5% p.a.

Answer: C

Simple interest of Rs. 800 over two years is Rs. 400 a year. Compound interest exceeds it by

\[ 840 - 800 = \text{Rs. } 40 \]

which is one year's interest on that first Rs. 400:

\[ 400 \times \frac{R}{100} = 40 \quad\Longrightarrow\quad R = 10\% \text{ p.a.} \]

The sum works out at Rs. 4000, and \( 4000(1.21 - 1) = 840 \) confirms it - but the principal is not needed to answer.

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