Simple Interest Questions and Answers

Answer: A

The time is 10 years. For the sum to become 1.5 times itself the interest must be half the sum, 4,800 rupees on Rs 9,600. Simple interest = 9600 x 5 x t / 100 = 480t, so 480t = 4800 and t = 10 years. 8, 11 and 12 years give interest of 3,840, 5,280 and 5,760 rupees. Here the interest needed is 50 per cent of the principal, and at 5 per cent a year each year earns 5 per cent of the principal, so the time is 50 divided by 5 = 10 years, whatever the principal is.

Answer: C

The amount is 6,655. At simple interest of 7.4 % for 5 years, the amount is the principal times 1 + 0.37 = 1.37.

\[ P = \frac{7535}{1.37} = 5500 \]

For one year at 20 % compounded half-yearly, the rate is 10 % for each of two half-years.

\[ A = 5500 \times (1.1)^2 = 5500 \times 1.21 = 6655 \]

The options 6,413, 6,534 and 7,920 do not equal 5500 times 1.21, so the third option is the answer. As a check, the interest in 5 years is 37 % of 5500, which is 2035, and 5500 + 2035 = 7535, the amount given in the question.

Answer: B

It will take 4 months.

Simple interest is P × R × T / 100. With P = 3500, R = 6 and an interest of 70, the time is

\[ T=\frac{70\times100}{3500\times6}=\frac{1}{3}\text{ year} \]

\[ \frac{1}{3}\text{ year}=4\text{ months} \]

2 months would earn 35, 8 months 140 and 6 months 105 as interest.

Per year the interest on 3500 at 6% is 210. A year therefore earns 210, a month earns 17.5 and 70 needs 4 months. The option '6 month' would earn 105 and 8 months would earn 140.

Answer: C

The sum is ₹ 9,600. Let the sum be \(P\). Simple interest for 10 years at 9.5% is \(0.95P\). The amount for \(3\frac{1}{2}\) years at 7% simple interest is \[ P\left(1 + \frac{7\times 3.5}{100}\right) = 1.245P \] The interest is less than that amount by 2,832: \[ 1.245P - 0.95P = 0.295P = 2832 \] \[ P = \frac{2832}{0.295} = 9600 \] Check: 0.95 × 9600 = 9120 and 1.245 × 9600 = 11952, which differ by 2832. The other sums do not give that difference.

Answer: A

The simple interest is 2176.

Simple interest = P × R × T / 100.

\[ \frac{6800\times8\times4}{100}=2176 \]

2167, 2076 and 2716 are different arrangements of the digits and do not equal the product.

The yearly interest is 8% of 6,800 = 544, and for 4 years it is 4 × 544 = 2,176. The principal is not added, since simple interest is only the interest. The amount would be 8,976.

Answer: A

1 only is correct.

Statement 1: at simple interest, doubling means the interest equals the principal: \(P \times r \times 10 / 100 = P\), so r = 10%. True.

Statement 2: at compound interest, \((1 + r)^{10} = 2\) gives \(r \approx 7.2\%\), since the interest itself earns interest. The rate needed is less than 10%, not more; at 10% compound a sum would grow to about 2.59 times in 10 years. False.

The rule of 72 gives the same answer quickly: \(72 / 10 \approx 7.2\%\).

Answer: B

The amount will be ₹ 8,250.

The interest is 1,200 in 4 years, so the rate is:

\[ \begin{aligned} R &= \frac{1200 \times 100}{6000 \times 4} = 5\% \\ R' &= 1.5 \times 5 = 7.5\% \end{aligned} \]

\[ SI = \frac{6000 \times 7.5 \times 5}{100} = 2250 \]

The amount is 6,000 + 2,250 = 8,250. 9,000 comes from using 10% (doubling the rate), and 8,000 and 9,250 from other slips.

Answer: B

The pair that is not correct is R = 15%, T = 7 years.

A sum doubles when the simple interest equals the principal:

\[ \begin{aligned} \frac{P \times R \times T}{100} &= P \\ \Rightarrow R \times T &= 100 \end{aligned} \]

Checking each option: 10 × 10 = 100, 25 × 4 = 100 and 5 × 20 = 100, so those three double the sum. But 15 × 7 = 105, which gives 105% interest, not exactly 100%.

Answer: A

He must invest the rest at 3.6% per annum.

Interest from the first two investments, and the amount left:

\[ \begin{aligned} 3500 \times 6\% &= 210 \\ 3000 \times 5\% &= 150 \\ \text{remaining} &= 9000 - 6500 = 2500 \\ \text{needed} &= 450 - 360 = 90 \\ \text{rate} &= \frac{90}{2500} \times 100 = 3.6\% \end{aligned} \]

3.5%, 3.8% and 3.9% would give yearly incomes of 87.50, 95 and 97.50 rupees from the remaining 2,500, so the total would not be exactly 450.

Answer: A

The rate is about 5 percent per annum.

From simple interest \(SI = \dfrac{P \times R \times T}{100}\):

\[ \begin{aligned} R &= \frac{100 \times SI}{P \times T} = \frac{100 \times 2850}{9530 \times 6} \\ &= \frac{285000}{57180} \approx 4.98 \end{aligned} \]

The exact figure is 4.98%, which rounds to 5%; on Rs 9,500 it would be exactly 5%. The other options are far off: at 7% the interest would be about Rs 4,000, and at 9% or 11% more still.