Simple Interest Questions and Answers

Answer: C

The rate is 12%.

With simple interest, the interest is the same every year. If the sum grows by 36% of itself in 3 years:

\[ \begin{aligned} R \times 3 &= 36 \\ R &= 12\% \end{aligned} \]

Check: 12% for 3 years is 36% of the principal. 9% and 10% give 27% and 30%, and 18% gives 54%.

Answer: C

The sum is ₹ 9500.

At 8% simple interest for 3 years, the interest is 24% of the principal, so the amount is 1.24 times it:

\[ \begin{aligned} 1.24P &= 11780 \\ P &= 9500 \end{aligned} \]

Check: 24% of ₹ 9,500 is ₹ 2,280, and 9,500 + 2,280 = 11,780. The other options give amounts of ₹ 10,540, ₹ 11,160 and ₹ 11,904.

Answer: B

It takes 12½ years.

An amount doubles when the simple interest equals the principal, so

\[ \begin{aligned} P &= \frac{P \times 8 \times T}{100} \\ T &= \frac{100}{8} = 12.5\ \text{years} \end{aligned} \]

A useful shortcut: at simple interest the time to double is 100 divided by the rate. 9 years is close to the 'rule of 72' for compound interest (72 / 8 = 9), which does not apply here; 13½ and 10½ years do not fit either rule.

Answer: D

The principal is Rs. 14,400.

At 8% simple interest for 5 years the interest is 40% of the principal, so the amount is 140% of it:

\[ \begin{aligned} P \times \frac{140}{100} &= 20160 \\ P &= \frac{20160 \times 100}{140} = 14400 \end{aligned} \]

Check: interest on 14,400 is 14,400 \(\times\) 8 \(\times\) 5 / 100 = 5,760, and 14,400 + 5,760 = 20,160. Rs. 14,440 is a near miss, and Rs. 14,000 would give only Rs. 19,600.

Answer: C

The extra principal is Rs 5,000, and its simple interest in 5 years is Rs 3,000, so \[\tfrac{5000\times5\times r}{100}=3000\] gives r = 12%, option C.

9.8%, 10% and 12.5% would give Rs 2,450, Rs 2,500 and Rs 3,125 on Rs 5,000.

Since only the difference of the principals matters, 3,000 is the simple interest on Rs 5,000 for 5 years, and the rate follows from 3,000 x 100 / (5,000 x 5) = 12. Testing the options confirms it, for 10 per cent would give Rs 2,500 and 12.5 per cent Rs 3,125 on Rs 5,000.

Answer: B

The simple interest for 2.5 years at 5% on Rs 6,400 is 6,400 x 0.05 x 2.5 = Rs 800, so the amount is 6,400 + 800 = Rs 7,200, option B.

800 is the interest alone, 640 is one year's interest at 10%, and 7,040 is the amount for 2 years.

Simple interest is P x r x t / 100, which gives 6,400 x 5 x 2.5 / 100 = 800. The question asks for the amount, which includes the principal, so 6,400 + 800 = 7,200. The options 800 and 640 are the interest on different bases and are not the amount.

Answer: C

Simple interest for the first two years is 15,600 x 10% x 2 = Rs 3,120, which is added to the principal, making Rs 18,720.

The interest for the next two years is 18,720 x 10% x 2 = Rs 3,744, the interest added at the end of the 4th year, option C. Rs 1,716 and Rs 1,872 are interest for one year on the wrong principal, and Rs 1,560 is one year's interest on the original principal.

The interest is added only after every second year, so the third and fourth years earn interest on the larger principal and the second block is bigger than the first.

Answer: B

The rate is 10% per annum.

If the sum doubles, the simple interest earned equals the principal \(P\) itself, over 10 years.

\[ \begin{aligned} \frac{P \times R \times 10}{100} &= P \\ R &= \frac{100}{10} = 10 \end{aligned} \]

The general rule: a sum doubles at simple interest in \(\frac{100}{R}\) years, so 10 years means 10%. At 8% doubling takes 12.5 years, at 12% about 8.3 years and at 15% about 6.7 years, so none of the other rates fits 10 years.

Answer: D

The simple interest is Rs. 711.25.

Simple interest is principal times rate times time, with 2 years 6 months written as 2.5 years:

\[ \begin{aligned} SI &= \frac{P \times R \times T}{100} \\ &= \frac{2276 \times 12.5 \times 2.5}{100} \\ &= 2276 \times 0.3125 = 711.25 \end{aligned} \]

The interest for one year is Rs. 284.50, so two and a half years gives \(284.50 \times 2.5 = 711.25\). The other amounts do not come from this rate and period; Rs. 569 would be the interest for exactly 2 years.

Answer: D

The simple interest is Rs. 624.

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

\[ \begin{aligned} SI &= \frac{P \times R \times T}{100} \\ &= \frac{5200 \times 6 \times 2}{100} \\ &= 624 \end{aligned} \]

Check: one year's interest at 6% on Rs. 5,200 is Rs. 312, and two years give twice that. Rs. 600 is what you get by rounding the principal to Rs. 5,000, and Rs. 524 or Rs. 450 come from arithmetic slips.