Question

harpreet borrowed rs 20000from her friend at 12% per annum simple interest she lent it to alam at the same rate but compounded annually find her gain after 2 years​

Answer 1

AnswEr :

$\bold{Given} \begin{cases} \underline{ \footnotesize\sf{ \star \: \: For\: Harpreet\: (SI)}} \\ \sf{Principal=Rs. 20000} \\ \sf{Rate=12 \% \: p.a.} \\ \sf{Time=2\: Yr. }\end{cases}$

$\bold{Given} \begin{cases} \underline{ \footnotesize\sf{ \star \: \: For\: Alam\: (CI)}} \\ \sf{Principal=Rs. 20000} \\ \sf{Rate=12 \% \: p.a.} \\ \sf{Time=2\: Yr. }\end{cases}$

Difference Betwⁿ Compound Interest and Simple Interest will be the Gain for Harpreet.

• Difference Between CI and SI will be :

$\leadsto\sf{Difference = Compound \: Interest - Simple \:Interest}$

$\leadsto\sf{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} -1 \bigg]- \bigg[\dfrac{PRT}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[20000\bigg(1 + \cancel\dfrac{12}{100} \bigg)^{2} - 1 \bigg]- \bigg[\dfrac{200 \cancel{00} \times 12 \times 2}{1\cancel{00}} }\bigg]$

$\leadsto\sf{Diff. = \bigg[20000\bigg(1 + \dfrac{3}{25} \bigg)^{2} - 1 \bigg]- \bigg[200 \times 12 \times 2}\bigg]$

$\leadsto\sf{Diff. = \bigg[20000\bigg(\dfrac{28}{25} \bigg)^{2} - 1 \bigg]- 4800}$

$\leadsto\sf{Diff. = \bigg[20000\bigg(\dfrac{784}{625} - 1\bigg)\bigg]- 4800}$

$\leadsto\sf{Diff. = \bigg[ \cancel{20000} \times \dfrac{159}{ \cancel{625}}\bigg]- 4800}$

$\leadsto\sf{Diff. =(32 \times 159) - 4800}$

$\leadsto\sf{Diff. =Rs.(5088 - 4800)}$

$\leadsto \large \boxed{\sf{Diff. =Rs. \: 288}}$

⠀

∴ Therefore, Harpreet will Gain Rs. 288

Answer 2

Answer:

Step-by-step explanation:

Given :-

Present value = Rs.20000

Interest rate = 12% per annum

Time = 2 years

To Find :-

Amount of money after 2 years.

Formula to be used :-

Simple interest (SI) = PRT/100

Amount (A) = $\bf P (1 + R/100)^n$

Solution :-

Putting all the values, we get

⇒ SI = (20000 × 12 × 2)/100

⇒ SI = 200 × 12 × 2

 ⇒ SI = 4800

Now,  we will  Amount

 ⇒ Amount (A) = $\bf P (1 + R/100)^n$

⇒ A = 20000 (1 + 12/100)2

⇒ A = 20000 (112/100)2

⇒ A = 20000 (1.12)2

⇒ A = 20000 × 1.2544

⇒ A = 25088

⇒ Compound interest = Rs.(25088 – 20000)

⇒ Compound interest   = Rs.5088

= (CI – SI)

= 5088 - 4800

= Rs.288

Hence, The amount of money Harpreet will gain after 2 years is Rs.288.