Compound Interest Questions and Answers

Answer: C

The compound interest is ₹ 2,050.

From the simple interest, \(2000 = P \times 0.05 \times 4\), so \(P = 10000\). Twice the principal is 20000, and compound interest for 2 years at 5% is:

\[ \begin{aligned} CI &= 20000\left[(1.05)^{2} - 1\right] \\ &= 20000 \times 0.1025 = 2050 \end{aligned} \]

Simple interest on 20000 for 2 years would be 2000; the extra 50 is the interest earned in the second year on the first year's interest of 1000. 2,250 would need a rate of about 5.5%.

Answer: A

Compounded annually, the amount is ₹ 15,840.

Half-yearly for 1½ years means 3 periods:

\[ \begin{aligned} \left(1 + \frac{r}{200}\right)^{3} &= \frac{15972}{12000} = 1{\cdot}331 = (1{\cdot}1)^{3} \\ \frac{r}{200} &= 0{\cdot}1 \Rightarrow r = 20\% \end{aligned} \]

Compounded annually, one full year at 20% is followed by half a year at simple interest of 10%:

\[ 12000 \times 1{\cdot}2 \times 1{\cdot}1 = 15840 \]

The amount is a little less than ₹ 15,972 because interest is added less often. ₹ 15,950 and ₹ 15,420 do not follow from a 20% rate, and ₹ 14,520 is the amount after only two half-years at 10%.

Answer: D

The amount is ₹ 12672.

First find the time from simple interest. The interest is 9500 - 8000 = 1500:

\[ \begin{aligned} 1500 &= \frac{8000 \times 7.5 \times x}{100} \\ 1500 &= 600x \\ x &= 2.5 \text{ years} \end{aligned} \]

At 20% compounded yearly for 2 years and then a half year at half the rate, 10%:

\[ \begin{aligned} A &= 8000 \times 1.2 \times 1.2 \times 1.1 \\ &= 11520 \times 1.1 = 12672 \end{aligned} \]

₹ 11520 would be the amount after only 2 years, and compounding for 3 full years would give ₹ 13824, which is option 1.

Answer: C

The value of x is 22,218.

For two full years compound the interest yearly; for the remaining third of a year, add simple interest at one third of the rate on the amount reached:

\[ \begin{aligned} A_2 &= 16000 \times (1.15)^{2} = 21160 \\ x &= 21160 \times \left(1 + \frac{0.15}{3}\right) \\ &= 21160 \times 1.05 = 22218 \end{aligned} \]

21,160 is the amount after only two years, before the final third of a year is added. The other figures do not follow from compounding yearly at 15% for two years and then adding interest for one third of a year.

Answer: B

The amount is ₹ 5,445.

First find the principal from the simple interest data. At 10% for 4 years, simple interest is 40% of the principal, so the amount is 1.4 times it:

\[ \begin{aligned} 1.4P &= 6300 \\ P &= 4500 \end{aligned} \]

Now compound it yearly for 2 years at 10%:

\[ \begin{aligned} A &= 4500 \times (1.1)^{2} \\ &= 4500 \times 1.21 = 5445 \end{aligned} \]

₹ 5,445 is ₹ 45 more than simple interest for 2 years would give (₹ 5,400), the interest earned on the first year's interest. The other options do not come from the correct principal.

Answer: C

The difference is ₹ 637.

Rajiv: 20% a year compounded half-yearly is 10% per half-year, for 3 half-years.

\[ \begin{aligned} A &= 7000 \times (1.1)^3 \\ &= 7000 \times 1.331 = 9317 \end{aligned} \]

So Rajiv's interest is ₹ 2,317. Amit: 10% a year compounded annually for 2 years.

\[ \begin{aligned} A &= 8000 \times (1.1)^2 \\ &= 8000 \times 1.21 = 9680 \end{aligned} \]

Amit's interest is ₹ 1,680, and \(2317 - 1680 = 637\). Treating Rajiv's investment as compounded yearly at 20% would give a quite different figure, which is why the half-yearly rate and period must both be halved and doubled.

Answer: C

The simple interest is ₹ 675.

First find the principal from the compound amount, then apply simple interest for 2.5 years:

\[ \begin{aligned} P(1.1)^2 &= 3267 \Rightarrow P = \frac{3267}{1.21} = 2700 \\ SI &= \frac{2700 \times 10 \times 2.5}{100} = 675 \end{aligned} \]

₹ 625, ₹ 650 and ₹ 700 come from a wrong principal or period; for example interest on 2,600 for 2.5 years would be 650.

Answer: B

The compound interest is 3570 rupees. First find the sum: at 10 % for 3 years compounded annually the factor is 1.331, so \[P = \frac{22627}{1.331} = 17000\] At double the rate, 20 % per annum, compounded half-yearly for one year means 10 % per half-year for 2 periods, a factor of 1.21: \[A = 17000 \times 1.21 = 20570\] Compound interest = 20570 - 17000 = 3570. The options 3360, 3780 and 3400 do not match this calculation.

Answer: A

The period is 2 years. The compound interest on Rs. 10,000 is Rs. 3456, so the amount is Rs. 13,456. Then \[ 10000\left(1 + \frac{16}{100}\right)^{n} = 13456 \] \[ 1.16^{n} = 1.3456 \] Since \(1.16^{2} = 1.3456\), \(n = 2\). For 3 years the amount would be \(10000\times 1.16^{3} = 15608.96\), which is too large, so the longer periods 3, 5 and 6 years are wrong.

Answer: A

The compound interest is Rs 5,716.22. For two years at 16 per cent compounded annually, the amount is the principal multiplied by 1.16 twice, and the interest is the amount less the principal.

\[ 1.16^2 = 1.3456 \]

\[ A = 16540 \times 1.3456 = 22256.22 \]

\[ CI = 22256.22 - 16540 = 5716.22 \]

The options 6,716.22 and 7,716.22 differ from this by whole thousands and do not come from the calculation, and 8,000 is a rounded figure that does not match 16 per cent for two years on this sum.