RD Sharma solution class 8 chapter 14 Compound Interest Exercise 14.1

Exercise 14.1

Page-14.4

Question 1:

Find the compound interest when principal = Rs 3000, rate = 5% per annum and time = 2 years.

Answer 1:

$$\begin{gathered} \mathrm{Principal} \mathrm{for} \mathrm{the} \mathrm{first} \mathrm{year}=\mathrm{Rs} 3,000 \\ \mathrm{Interest} \mathrm{for} \mathrm{the} \mathrm{first} \mathrm{year}=\mathrm{Rs}\left(\frac{3,000\times 5\times 1}{100}\right) \\ =\mathrm{Rs} 150 \\ \mathrm{Amount} \mathrm{at} \mathrm{the} \mathrm{end} \mathrm{of} \mathrm{the} \mathrm{first} \mathrm{year}=\mathrm{Rs} 3,000+\mathrm{Rs} 150 \\ =\mathrm{Rs} 3,150 \\ \mathrm{Principal} \mathrm{for} \mathrm{the} \mathrm{second} \mathrm{year}=\mathrm{Rs} 3,150 \\ \mathrm{Interest} \mathrm{for} \mathrm{the} \mathrm{second} \mathrm{year}=\mathrm{Rs}\left(\frac{3,150\times 5\times 1}{100}\right) \\ =\mathrm{Rs} 157.50 \\ \mathrm{Amount} \mathrm{at} \mathrm{the} \mathrm{end} \mathrm{of} \mathrm{the} \mathrm{second} \mathrm{year}=\mathrm{Rs} 3,150+\mathrm{Rs} 157.50 \\ =\mathrm{Rs} 3307.50 \\ \therefore \mathrm{Compound} \mathrm{interest}=\mathrm{Rs}\left(3,307.50-3,000\right) \\ =\mathrm{Rs} 307.50 \end{gathered}$$

Question 2:

What will be the compound interest on Rs 4000 in two years when rate of interest is 5% per annum?

Answer 2:

$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{amount} \mathrm{A} \mathrm{at} \mathrm{the} \mathrm{end} \mathrm{of} \mathrm{n} \mathrm{years} \mathrm{at} \mathrm{the} \mathrm{rate} \mathrm{of} \mathrm{R}\% \mathrm{per} \mathrm{annum} \mathrm{is} \mathrm{given} \mathrm{by} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}. \\ \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 4,000 \\ \mathrm{R}=5\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=2 \mathrm{years} \\ \mathrm{Now}, \\ \mathrm{A}=4,000{\left(1+\frac{5}{100}\right)}^2 \\ =4,000{\left(1.05\right)}^2 \\ =\mathrm{Rs} 4,410 \\ \mathrm{And}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 4,410-\mathrm{Rs} 4,000 \\ =\mathrm{Rs} 410 \end{gathered}$$

Question 3:

Rohit deposited Rs 8000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3 years?

Answer 3:

$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{amount} \mathrm{A} \mathrm{at} \mathrm{the} \mathrm{end} \mathrm{of} \mathrm{n} \mathrm{years} \mathrm{at} \mathrm{the} \mathrm{rate} \mathrm{of} \mathrm{R}\% \mathrm{per} \mathrm{annum} \mathrm{is} \mathrm{given} \mathrm{by} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}. \\ \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 8,000 \\ \mathrm{R}=15\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=3 \mathrm{years} \\ \mathrm{Now}, \\ \mathrm{A}=8,000{\left(1+\frac{15}{100}\right)}^3 \\ =8,000{\left(1.15\right)}^3 \\ =\mathrm{Rs} 12,167 \\ \mathrm{And}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 12,167-\mathrm{Rs} 8,000 \\ =\mathrm{Rs} 4,167 \end{gathered}$$

Question 4:

Find the compound interest on Rs 1000 at the rate of 8% per annum for $1\frac{1}{2}$ years when interest is compounded half-yearly.

Answer 4:

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 1,000 \\ \mathrm{R}=8\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=1.5 \mathrm{years} \\ \mathrm{We} \mathrm{know} \mathrm{that}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{2\mathrm{n}} \\ =1,000{\left(1+\frac{8}{200}\right)}^3 \\ =1,000{\left(1.04\right)}^3 \\ =\mathrm{Rs} 1,124.86 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 1,124.86-\mathrm{Rs} 1,000 \\ =\mathrm{Rs} 124.86 \end{gathered}$$

Question 5:

Find the compound interest on Rs 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.

Answer 5:

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 16,000 \\ \mathrm{R}=20\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=1 \mathrm{year} \\ \mathrm{We} \mathrm{know} \mathrm{that}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{400}\right)}^{4\mathrm{n}} \\ =16,000{\left(1+\frac{20}{400}\right)}^4 \\ =16,000{\left(1.05\right)}^4 \\ =\mathrm{Rs} 19,448.1 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 19,448.1-\mathrm{Rs} 16,000 \\ =\mathrm{Rs} 3,448.1 \end{gathered}$$

Page-14.5

Question 6:

Swati took a loan of Rs 16000 against her insurance policy at the rate of $12\frac{1}{2}\%$ per annum. Calculate the total compound interest payable by Swati after 3 years.

Answer 6:

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 16,000 \\ \mathrm{R}=12.5\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=3 \mathrm{years} \\ \mathrm{We} \mathrm{know} \mathrm{that}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =16,000{\left(1+\frac{12.5}{100}\right)}^3 \\ =16,000{\left(1.125\right)}^3 \\ =\mathrm{Rs} 22,781.25 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 22,781.25-\mathrm{Rs} 16,000 \\ =\mathrm{Rs} 6,781.25 \end{gathered}$$

Question 7:

Roma borrowed Rs 64000 from a bank for $1\frac{1}{2}$ years at the rate of 10% per annum. Compute the total compound interest payable by Roma after $1\frac{1}{2}$ years, if the interest is compounded half-yearly.

Answer 7:

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 64,000 \\ \mathrm{R}=10\% \mathrm{p}.\mathrm{a}. \\ \mathrm{n}=1.5 \mathrm{years} \\ \mathrm{Amount} \mathrm{after} \mathrm{n} \mathrm{years}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{200}\right)}^{2\mathrm{n}} \\ =64,000{\left(1+\frac{10}{200}\right)}^3 \\ =64,000{\left(1.05\right)}^3 \\ =\mathrm{Rs} 74,088 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 74,088-\mathrm{Rs} 64,000 \\ =\mathrm{Rs} 10,088 \end{gathered}$$

Question 8:

Mewa Lal borrowed Rs 20000 from his friend Rooplal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.

Answer 8:

$$\begin{gathered} \mathrm{SI} \mathrm{for} \mathrm{Mewa} \mathrm{Lal}=\frac{\mathrm{PRT}}{100} \\ =\frac{20,000\times 18\times 2}{100} \\ =\mathrm{Rs} 7,200 \\ \mathrm{Thus}, \mathrm{he} \mathrm{has} \mathrm{to} \mathrm{pay} \mathrm{Rs} 7,200 \mathrm{as} \mathrm{interest} \mathrm{after} \mathrm{borrowing}. \\ \mathrm{CI} \mathrm{for} \mathrm{Mewa} \mathrm{Lal} = \mathrm{A}-\mathrm{P} \\ =20,000{\left(1+\frac{18}{100}\right)}^2-20,000 \\ =20,000{\left(1.18\right)}^2-20,000 \\ =27,848-20,000 \\ =\mathrm{Rs} 7,848 \\ \mathrm{He} \mathrm{gained} \mathrm{Rs} 7,848 \mathrm{as} \mathrm{interest} \mathrm{after} \mathrm{lending}. \\ \mathrm{His} \mathrm{gain} \mathrm{in} \mathrm{the} \mathrm{whole} \mathrm{transaction}=\mathrm{Rs} 7,848-\mathrm{Rs} 7,200 \\ =\mathrm{Rs} 648 \end{gathered}$$

Question 9:

Find the compound interest on Rs 8000 for 9 months at 20% per annum compounded quarterly.

Answer 9:

$$\begin{gathered} \mathrm{P}=\mathrm{Rs} 8,000 \\ \mathrm{T}=9 \mathrm{months}=3 \mathrm{quarters} \\ \mathrm{R}=20\% \mathrm{per} \mathrm{annum}=5\% \mathrm{per} \mathrm{quarter} \\ \mathrm{A}=8,000{\left(1+\frac{5}{100}\right)}^3 \\ =8,000{\left(1.05\right)}^3 \\ =9,261 \\ \mathrm{The} \mathrm{required} \mathrm{amount} \mathrm{is} \mathrm{Rs} 9,261. \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 9,261-\mathrm{Rs} 8,000 \\ =\mathrm{Rs} 1,261 \end{gathered}$$

Question 10:

Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the rate of 10% per annum gives Rs 200 as simple interest.

Answer 10:

$$\begin{gathered} \mathrm{SI}=\frac{\mathrm{PRT}}{100} \\ \therefore \mathrm{P}=\frac{\mathrm{SI}\times 100}{\mathrm{RT}} \\ =\frac{200\times 100}{10\times 2} \\ =\mathrm{Rs} 1,000 \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =1,000{\left(1+\frac{10}{100}\right)}^2 \\ =1,000{\left(1.10\right)}^2 \\ =\mathrm{Rs} 1,210 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 1,210-\mathrm{R}s 1,000 \\ =\mathrm{Rs} 210 \end{gathered}$$

Question 11:

Find the compound interest on Rs 64000 for 1 year at the rate of 10% per annum compounded quarterly.

Answer 11:

$$\begin{gathered} \mathrm{To} \mathrm{calculate} \mathrm{the} \mathrm{interest} \mathrm{compounded} \mathrm{quarterly}, \mathrm{we} \mathrm{have}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{400}\right)}^{4\mathrm{n}} \\ =64,000{\left(1+\frac{10}{400}\right)}^{4\times 1} \\ =64,000{\left(1.025\right)}^4 \\ =70,644.03 \\ \mathrm{Thus}, \mathrm{the} \mathrm{required} \mathrm{amount} \mathrm{is} \mathrm{Rs} 70,644.03. \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 70,644.025-\mathrm{Rs} 64,000 \\ =\mathrm{Rs} 6,644.03 \end{gathered}$$

Question 12:

Ramesh deposited Rs 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months.

Answer 12:

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{P}=\mathrm{Rs} 7,500 \\ \mathrm{R}=12\% \mathrm{p}.\mathrm{a}.=3\% \mathrm{quarterly} \\ \mathrm{T}=9 \mathrm{months}=3 \mathrm{quarters} \\ \mathrm{We} \mathrm{know} \mathrm{that}: \\ \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ \mathrm{A}=7,500{\left(1+\frac{3}{100}\right)}^3 \\ =7,500{\left(1.03\right)}^3 \\ =8,195.45 \\ \mathrm{Thus}, \mathrm{the} \mathrm{required} \mathrm{amount} \mathrm{is} \mathrm{Rs} 8,195.45. \end{gathered}$$

Question 13:

Anil borrowed a sum of Rs 9600 to install a handpump in his dairy. If the rate of interest is $5\frac{1}{2}\%$ per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.

Answer 13:

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =9,600{\left(1+\frac{5.5}{100}\right)}^3 \\ =9,600{\left(1.055\right)}^3 \\ =\mathrm{Rs} 11,272.72 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 11,272.72-\mathrm{Rs} 9,600 \\ =\mathrm{Rs} 1,672.72 \end{gathered}$$

Question 14:

Surabhi borrowed a sum of Rs 12000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.

Answer 14:

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =12,000{\left(1+\frac{5}{100}\right)}^3 \\ =12,000{\left(1.05\right)}^3 \\ =13,891.50 \\ \mathrm{Thus}, \mathrm{the} \mathrm{required} \mathrm{amount} \mathrm{is} \mathrm{Rs} 13,891.50. \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 13,891.50-\mathrm{Rs} 12,000 \\ =\mathrm{Rs} 1,891.50 \end{gathered}$$

Question 15:

Daljit received a sum of Rs. 40000 as a loan from a finance company. If the rate of interest is 7% per annum compounded annually, calculate the compound interest that Daljit pays after 2 years.

Answer 15:

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}} \\ =40,000{\left(1+\frac{7}{100}\right)}^2 \\ =40,000{\left(1.07\right)}^2 \\ =45,796 \\ \mathrm{Thus}, \mathrm{the} \mathrm{required} \mathrm{amount} \mathrm{is} \mathrm{Rs} 45,796. \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs} 45,796-\mathrm{Rs} 40,000 \\ =\mathrm{Rs} 5,796 \end{gathered}$$