ML AGGARWAL CLASS 8 CHAPTER 8 Simple and Compound Interest Exercise 8.2

Exercise 8.2

Question 1

Sol :

Given 

principal p = 6000

Rate R = 10 % 

Time T = 2 Year 

Interest for first year = $\frac{P T R}{100}$

$\frac{6000 \times 4 \times 10}{100}$

$I_{1}$ = 6000

Amount at the end of the First year =6000+600

Principal for second year =266001

Interest for Second year $=\frac{P T R}{100}$

$=\frac{6600 \times 1 \times 10}{100}$

$I_{2}=660$

$\begin{aligned} \text { Amount at the end of second yean } &=6600+660 \\ &=7260 /-\end{aligned}$

∴ Compound interest for 2 year = final amount - (original) principal

= 7260 - 6000

= 1260

Question 2

Sol- 

$\begin{aligned} \text { Principal for first } \operatorname{year}\left(P_{1}\right)=& ₹ 1875 /-\\ \text { Rate }(R)=4 \% & \text { Time }(T)=2 \text { years. } \\ \text { Interest for first year }\left(I_{1}\right)=\frac{P_{1} \times T_{1} \times R}{100} \\=& \frac{1875 \times 1 \times 4}{100} \\ I_{1}=& ₹ 75\end{aligned}$

Amount at the end of first year =1875+75

=1950

Interest for Second your $I_{2}=\frac{1950 \times 1 \times 4}{100}$

$I_{2}=78 /-$

$\therefore$ Compound Interest after 2 year $=I_{1}+I_{2}$

$\begin{array}{l}=75+78 \\=153\end{array}$

 Hence, Salma has to pay 2153 as compound Interest to the Mahila samit

Question 3

Sol :

Principal for first year $\left(R_{1}\right)=12000$

$Rate=10 \%, \text { Time }=3 \text { years }$

$\begin{aligned} \text { interest for first year }\left(I_{1}\right) &=\frac{12000 \times 1 \times 10}{100} \\ I_{1} &=₹ 1200\end{aligned}$

Total amount at the end of first year 12000+1200

=13200

principal for second year = Rs 13200 

interest for second year $I_{2}=$ $\frac{13200 \times 1 \times 10}{100}$

=₹ 1320 

Total amount at the end of the second year is 13200 + 1320 = Rs 14520

Principal amount for third year = Rs 14520

Interest for third year $I_{3}=\frac{14520 \times 1 \times 10}{100}$

$I_{3}=₹ 1452$

$\begin{aligned} \text { Total amount at the end of third year } &=14520+1452 \\ &=₹ 15972 \end{aligned}$

$\begin{aligned} \text { Compound Interest for } 3 \text { years } &=\text { Final amount }-\text { Principal }\left(P_{1}\right) \\ &=15972-12000 \\ &=23972 \end{aligned}$

Hence , At the end of 3 year jacob will get total 

Amount as Rs 15972 and compound interest Rs 3972 

Question 4

Sol :

Given

Principal $\left(P_{1}\right)=46875$

Rate (R)=4 %, Time =3 years.

principal amount for first year $\left(p_{1}\right)$ = Rs 46875 

Rate (R) = 4 % time = 3 years

(i) Interest for first year $\left(I_{1}\right)$

$I_{1}=1875$

$\begin{aligned} \text { Total amount at the end of Girst year } &=46875+1875 \\ &=48750 \end{aligned}$

Principal amount for second $\operatorname{year}\left(R_{2}\right)=$ 2 48750

Interest for Second year $\left(I_{2}\right)=\frac{48750 \times 4 \times 1}{100}$

$I_{2}$= Rs 21950

(ii) Total amount at the end of second year

= 48750 + 1950

= Rs 50700

Principal for third year $\left(P_{3}\right)$=  Rs 50700

(iii) $\begin{aligned} \text { Interest for third year }\left(I_{3}\right) &=\frac{50700 \times 1 \times 4}{100} \\ &=2028 \end{aligned}$

Hence ,

(i) The interest for first year $=21875$

(ii) The Amount standing to his credit at the end of

second year is  Rs 50700

(iii) The interest for third year =Rs  2028

Question 5

Sol :

Given 

Principal =260001 , Time =3 years

Rate =10

Principal amount for first $\operatorname{year}\left(P_{1}\right)=26000$

Interest for first year $\left(I_{1}\right)=\frac{6000 \times 1 \times 10}{100}$

Total amount at the end of first year 6000+600

=6600

Principal for second year $\left(P_{2}\right)=6600$

(i)  Interest for second year $\left(I_{2}\right)=\frac{6600 \times 1 \times 10}{100}$

$I_{2}=₹ 660$

Total amount at the end of second year =6600+660

=7260

$\begin{array}{ll}\text { Principal for third year } & \left(P_{3}\right)=27260 \\ \text { Interest for Third year } & \left(-I_{3}\right)=\frac{7260 \times 1 \times 10}{100} \\ & I_{3}=726 /-\end{array}$

(ii) Total amount at the end of third year = 7260 + 726

= Rs 7986

 hence 

(i) Compound interest for second year = Rs 660

(ii) Total amount at the end of the third year = Rs 7986

Question 6

Sol :

principal amount for first year $\left(P_{1}\right)$=Rs 5000

Rate of interest for first year $\left(R_{1}\right)=6 \%$

$\begin{aligned} \text { Interest for first year } &=\frac{5000 \times 1 \times 6}{100} \\\left(I_{1}\right) &=300 \end{aligned}$

$\begin{aligned} \text { Total amout at the end of first year } &=5000+300 \\ &=5300\\ \text { Principal amourt for second year }\left(P_{2}\right)=& 5300 \\ \text { Rate of Interest for Second year} &=8 \% . \\ \text { Compomd Interest for Second year } &=\frac{5300 \times 1 \times 8}{100} \end{aligned}$

$\left(I_{2}\right)=424$

$\begin{aligned} \text { Total amount at the end of second year } &=5300+424 \\ &= 5724 \end{aligned}$

$\begin{aligned} \text { Compound interest for } 2 \text { years } &=\text { final amount }-\text { Principal }\left(P_{1}\right) \\ &=5724-5000 \\ &=₹ 724 \end{aligned}$

Hence total amount after 2 year = Rs 5724

Compound interest for 2 year = Rs 724

Question 7

Sol :

Given principal = Rs 20000

Time = 2 year 

Rate of interest = 8%

Simple Interest $(I)=\frac{P T R}{100}$

$=\frac{20000 \times 2 \times 8}{100}$

Simple Interest (I.)=33200

Let compound interest as 'C'

Interest for first year = $\frac{20000 \times 1 \times 8}{100}$

$I_{1}=1600$

Total amount at the end of first year = 20000+ 1600

= 21600

Compound interest for 2 year = $I_{1}+I_{2}$

=1600+1728

C=3328

∴ Difference between the compound interest and 

simple interest is (c - I ) =  3328 - 3200

 = Rs 128