Compound Interest Questions and Answers

Answer: B

The compound interest is Rs 66,351. Compounded half-yearly for 2 years at 8% a year means 4 periods at 4%.

Rs 456976 is the amount, not the interest. Simple interest would be Rs 62,500, and the other options do not equal the compound interest.

The step of halving the rate and doubling the periods is the key to half-yearly compounding: 8% a year becomes 4% for each of the four half-years. The amount is 390625 × 1.04 four times over, which is Rs 4,56,976, and the compound interest is the amount minus the principal. Rs 66,351 is therefore the interest and Rs 4,56,976 is not.

Answer: A

The compound interest is Rs 512.50. The amount is 5000 x 1.05 x 1.05 = 5512.50 so the interest is 5512.50 - 5000 = 512.50. Rs 500 is simple interest for one year, and Rs 510.50, 500.50 and 511.50 do not match the compounding of 5 per cent for two years. The square of 1.05 is 1.1025, so the compound interest rate for two years is 10.25 per cent of Rs 5,000, which is Rs 512.50. Simple interest would be only Rs 500, so the compound interest is larger by the interest earned on the first year's interest, Rs 12.50.

Answer: A

With compound interest the amount grows by the same factor in each equal period. It becomes 3 times in 5 years, so after the next 5 years it is 3 x 3 = 9 times, and after another 5 years it is 9 x 3 = 27 times. So it takes 3 periods of 5 years, which is 15 years, option (A). The options 20, 25 and 30 years would give 81 times, 243 times and 729 times, which are more than 27 times. In general, if a sum becomes k times in n years, it becomes k to the power m times in m x n years, which here gives 3 cubed, 27, in 3 x 5 years.

Answer: D

The compound interest is 4,634. In one year at 10 % compounded half-yearly, the rate is 5 % per half-year for two half-years, so the amount is the principal times 1.1025.

\[ P = \frac{15435}{1.1025} = 14000 \]

Compounded yearly for 3 years at 10 %:

\[ CI = 14000 \times (1.1^3 - 1) \]

\[ = 14000 \times 0.331 = 4634 \]

The options 4,524, 4,554 and 4,624 do not equal 14000 times 0.331, so the fourth option is correct. As a check, 14000 x 1.1025 = 15435, the amount given in the question, and the amount after 3 years at yearly compounding is 14000 x 1.331 = 18634.

Answer: B

The total interest charged is ₹ 616. The rate per half-year is 4%. Let each instalment be \(x\); the present value of the two instalments equals the loan: \[ \frac{x}{1.04} + \frac{x}{1.04^{2}} = 10200 \] \[ x\times\frac{1.04 + 1}{1.0816} = 10200 \] \[ x = \frac{10200\times 1.0816}{2.04} = 5408 \] Total paid is \(2\times 5408 = 10816\), so the interest is \(10816 - 10200 = 616\). Simple interest at 8% for one year on 10,200 would be 816, which is not the compounded two-instalment figure.

Answer: A

C.I. when interest is compounded yearly 

= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100] 

= 5000 * 26/25 * 51/50 = Rs. 5304 

C.I. when interest is compounded half-yearly 

= [5000 * (1 + 2/100)²] 

= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304) = Rs. 2.04

Answer: C

Let the rate of interest be R% p.a. 

4400{[1 + R/100]² - 1} = 11193.60 

[1 + R/100]² = (44000 + 11193.60)/44000

[1 + R/100]² = 1 + 2544/1000 = 1 + 159/625 

[1 + R/100]² = 784/625 = (28/25)2 

1 + R/100 = 28/25 

R/100 = 3/25 

Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100 

=Rs.10560

Answer: A

Over two years the gap between compound and simple interest is

\[ \text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^{2} \]

\[ 96 = 15000 \times \frac{R^{2}}{10000} = 1.5R^{2} \]

\[ R^{2} = 64 \quad\Longrightarrow\quad R = 8\% \]

The rate is fully determined, so "cannot be determined" is a trap: for a two-year period the difference, the principal and the rate are locked together by that single relation.

Answer: D

Compound growth is multiplicative, so doubling twice is the same as quadrupling.

\[ \left(1 + \frac{R}{100}\right)^{9} = 2 \]

\[ \left(1 + \frac{R}{100}\right)^{18} = \left[\left(1 + \frac{R}{100}\right)^{9}\right]^{2} = 2^{2} = 4 \]

So it takes 18 years. The rate never needs to be found.

This multiplicative behaviour is what separates compound from simple interest: under simple interest, doubling in 9 years means quadrupling in 27, since there the growth is additive.

Answer: B

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

Half-yearly compounding at 5% per annum means 2.5% per half-year. The January deposit earns for two half-years and the July deposit for one.

\[ A = 1600(1.025)^{2} + 1600(1.025) \]

\[ = 1600(1.050625) + 1640 = 1681 + 1640 = \text{Rs. } 3321 \]

\[ \text{interest} = 3321 - 3200 = \text{Rs. } 121 \]

Each deposit must be tracked from its own date; treating the full Rs. 3200 as present all year would give Rs. 162.