Simple Interest Questions and Answers

Answer: A

The amount is Rs. 1,380.

\[ \begin{aligned} \text{SI} &= \frac{1200 \times 5 \times 3}{100} = 180 \\ \text{Amount} &= 1200 + 180 = 1380 \end{aligned} \]

Rs. 1,260 would be the amount after one year only, and Rs. 1,290 and Rs. 1,240 do not match 5% simple interest for three years. Rs. 1,470 comes from a much higher rate.

Simple interest is earned only on the original principal, so it is the same Rs. 60 in each of the three years.

Answer: C

The rate of interest was 10% p.a.

Using \(\text{SI} = \frac{P \times R \times T}{100}\):

\[ \begin{aligned} R &= \frac{100 \times \text{SI}}{P \times T} \\ &= \frac{100 \times 1500}{5000 \times 3} = 10 \end{aligned} \]

Check: 10% of Rs. 5,000 is Rs. 500 a year, and three years give Rs. 1,500. At 8%, 9% or 11% the interest would be Rs. 1,200, Rs. 1,350 or Rs. 1,650.

The formula rearranges as \(R = \frac{100 \times \text{SI}}{P \times T}\), so the rate can be read off directly once the interest, principal and time are known.

Answer: B

The rate is 8% per annum.

Simple interest is \(SI = \frac{P \times R \times T}{100}\). Here \(SI = \frac{2}{5}P\) and \(T = 5\) years.

\[ \begin{aligned} \tfrac{2}{5}P &= \frac{P \times R \times 5}{100} \\ R &= \frac{2}{5} \times \frac{100}{5} \\ &= 8 \end{aligned} \]

Check: at 8% for 5 years the interest is 40% of the sum, which is \(\frac{2}{5}\). 10% would give half the sum, and 6% gives 30%.

Answer: B

The interest is ₹ 1,200.

Simple interest is principal times rate times time, divided by 100:

\[ SI = \frac{5000 \times 8 \times 3}{100} = 1200 \]

So the interest after 3 years is ₹ 1,200. Each year earns ₹ 400 (8% of 5,000), and three years earn three times that.

₹ 1,000 and ₹ 1,400 do not match any whole number of years at ₹ 400 a year, and ₹ 1,800 would need 4.5 years.

Answer: C

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

\[ \text{SI} = 15600 - 12000 = \text{Rs. } 3600 \]

\[ 3600 = \frac{12000 \times 6 \times T}{100} = 720\,T \]

\[ T = 5 \text{ years} \]

The Rs. 15,600 is the amount, so the principal must be subtracted before the formula can be used.

Answer: B

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

\[ 9600 = \frac{P \times 16 \times 5}{100} = 0.8P \]

\[ P = \frac{9600}{0.8} = \text{Rs. } 12{,}000 \]

Over five years at 16% the interest comes to 80% of the loan, which is why the principal is only a little above the interest itself.

Answer: A

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

The two deposits share one rate \( r \), so add their interests.

\[ \frac{500 \times r \times 2}{100} + \frac{300 \times r \times 4}{100} = 220 \]

\[ 10r + 12r = 220 \quad\Longrightarrow\quad 22r = 220 \]

\[ r = 10\% \]

Checking: Rs. 100 from SBI and Rs. 120 from ICICI.

Answer: C

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

The rate changes with the period, so add the three slabs. Beyond five years leaves \( 9 - 5 = 4 \) years at 14%.

\[ P\left(\frac{6 \times 2}{100} + \frac{9 \times 3}{100} + \frac{14 \times 4}{100}\right) = 11400 \]

\[ P(0.12 + 0.27 + 0.56) = 0.95P = 11400 \]

\[ P = \text{Rs. } 12{,}000 \]

The final slab runs for four years, not nine - "beyond five years" means the remainder of the nine.

Answer: A

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

Find the original rate first.

\[ \text{SI} = 2600 - 2000 = 600 \quad\Longrightarrow\quad 600 = \frac{2000 \times R \times 5}{100} = 100R \]

\[ R = 6\% \]

At \( 6 + 3 = 9\% \):

\[ \text{SI} = \frac{2000 \times 9 \times 5}{100} = 900 \quad\Longrightarrow\quad \text{amount} = \text{Rs. } 2900 \]

The extra 3% over 5 years adds \( 2000 \times 0.15 = 300 \) - the same answer in one step.

Answer: D

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

The Rs. 8470 is the amount, which is the principal plus nine years of interest.

\[ 8470 = P\left(1 + \frac{6 \times 9}{100}\right) = P(1.54) \]

\[ P = \frac{8470}{1.54} = \text{Rs. } 5500 \]

Checking: the interest is \( 5500 \times 0.54 = 2970 \), and \( 5500 + 2970 = 8470 \).