Question

Calculate simple interest and compound interest on Rs. 100000 at 10% per
annum for 5 consecutive years and tabulate the data in the following manner.
​

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Principal=Rs. 100000} \\ \sf{Rate=10\% \: p.a.}\\ \sf{Time=5\: Yr. }\end{cases}$

• First Let's Calculate Simple Interest :

$\underline{\star \: \text{For 1st Year :}}$

$\longrightarrow \sf SI = \dfrac{P \times r \times t}{100}$

$\longrightarrow \sf SI = \dfrac{1000 \cancel{00} \times 10 \times 1}{\cancel{100}}$

$\longrightarrow \sf SI = 1000 \times 10 \times 1$

$\longrightarrow \sf SI = Rs.10000$

$\rule{300}{1}$

$\underline{\star \: \text{For 2nd Year :}}$

$\longrightarrow \sf SI = \dfrac{P \times r \times t}{100}$

$\longrightarrow \sf SI = \dfrac{1000 \cancel{00} \times10 \times 1}{\cancel{100}}$

$\longrightarrow \sf SI = 1000 \times 10 \times1$

$\longrightarrow \sf SI= Rs.10000$

$\rule{300}{1}$

$\text{We can notice that neither Principal Changes}$

$\text{nor rate therefore Interest will be Same for Each}$

$\text{Consecutive Year in Simple Interest i.e. Rs. 10000}$

⇒ SI for 5 Years = 5 × 10,000

⇒ SI for 5 Years = Rs. 50,000

$\rule{300}{2}$

• Now Let's Calculate Compound Interest :

$\underline{\star \: \text{For 1st Year:}}$

$\longrightarrow \sf CI = P \times \dfrac{r}{100}$

$\longrightarrow \sf CI = 1000\cancel{00} \times \dfrac{10}{\cancel{100}}$

$\longrightarrow \sf CI = 1000 \times 10$

$\longrightarrow \sf CI =Rs.10000$

$\rule{300}{1}$

$\underline{\star \: \text{For 2nd Year :}}$

$\longrightarrow \sf CI = (P + CI)\times \dfrac{r}{100}$

$\longrightarrow \sf CI = (100000 + 10000)\times \dfrac{10}{100}$

$\longrightarrow \sf CI = 1100\cancel{00} \times \dfrac{10}{\cancel{100}}$

$\longrightarrow \sf CI = 1100 \times 10$

$\longrightarrow \sf CI =Rs.11000$

$\rule{300}{1}$

$\underline{\star \: \text{For 3rd Year :}}$

$\longrightarrow \sf CI = (P + CI)\times \dfrac{r}{100}$

$\longrightarrow \sf CI = (110000 + 11000)\times \dfrac{10}{100}$

$\longrightarrow \sf CI = 1210\cancel{00} \times \dfrac{10}{\cancel{100}}$

$\longrightarrow \sf CI = 1210 \times 10$

$\longrightarrow \sf CI =Rs.12100$

$\rule{300}{1}$

$\underline{\star \: \text{For 4th Year :}}$

$\longrightarrow \sf CI= (P + CI)\times \dfrac{r}{100}$

$\longrightarrow \sf CI = (121000 + 12100)\times \dfrac{10}{100}$

$\longrightarrow \sf CI = 1331\cancel{00} \times \dfrac{10}{\cancel{100}}$

$\longrightarrow \sf CI = 1331\times 10$

$\longrightarrow \sf CI =Rs.13310$

$\rule{300}{1}$

$\underline{\star \: \text{For 5th Year :}}$

$\longrightarrow \sf CI=(P + CI)\times \dfrac{r}{100}$

$\longrightarrow \sf CI = (133100 + 13310)\times \dfrac{10}{100}$

$\longrightarrow \sf CI = 14641\cancel{0} \times \dfrac{\cancel{10}}{\cancel{100}}$

$\longrightarrow \sf CI =Rs.14641$

$\text{We can Notice that Principal for each consecutive}$

$\text{year is (CI + Principal of next year) and Rate is Same.}$

⇒ CI for 5 Years = 10,000 + 11,000 + 12,100 + 13,310 + 14,641

⇒ CI for 5 Years = Rs. 61,051

$\rule{300}{2}$

$\begin{tabular}{|c|c|c|c|c|}\cline{1-5}\multicolumn{5}{|c|}{Bar Graph Representation} \\\cline{1-5} Year & Principal for SI & Principal for CI & SI & CI \\\cline{1-5} 1 & 100000 & 100000 & 10000 & 10000 \\2 & 100000 & 110000 & 10000 & 11000 \\ 3 & 100000 & 121000 & 10000 & 12100 \\4 & 100000 & 133100 & 10000 & 13310 \\5 & 100000 & 146410 & 10000 & 146411 \\ \cline{1-5}\end{tabular}$

Answer 2

Answer:

• Simple Interest = Rs. 50,000

• Compound Interest = Rs. 61,051

Step-by-step explanation:

=> SI = Prt/100

=> SI = (100,000*10*5)/100

=> SI = Rs. 1000*10*5

=> SI = Rs. 50,000

=> CI = P{(1 + r/100)ⁿ - 1}

=> CI = 100,000*{(1 + 10/100)⁵ - 1)}

=> CI = 100,000*{(1 + 1/10)⁵ - 1)}

=> CI = 100,000*{(11/10)⁵ - 1}

=> CI = 100,000*(161,051 - 100,000)/100,000

=> CI = Rs. 61,051