Question

find the principal which will amount to 4500 in 2 years at rate of 4% per annum compounded annually

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{Amount = Rs. \:4500}\\\sf{Time = 2 \:Years}\\ \sf{Rate = 4\% \:p.a.}\\\sf{Principal = ?} \end{cases}$

• Amount of the Compound Interest :

$\longrightarrow \sf{Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}} \\ \\\longrightarrow \sf{4500 = P \times \bigg(1 +\cancel\dfrac{4}{100} \bigg)^{2}} \\ \\\longrightarrow \sf{4500 = P \times \bigg(1 +\dfrac{1}{25} \bigg)^{2}} \\ \\\longrightarrow \sf{4500 = P \times \bigg(\dfrac{25 + 1}{25} \bigg)^{2}}\\ \\\longrightarrow \sf{4500 = P \times \bigg(\dfrac{26}{25} \bigg)^{2}} \\ \\\longrightarrow \sf{4500 = P \times \dfrac{676}{625}} \\ \\\longrightarrow \sf{4500 \times \dfrac{625}{676} = P} \\ \\\longrightarrow \sf{ \dfrac{2812500}{676} = P} \\ \\\longrightarrow \large \boxed{\sf{P = Rs. \:4160.50 }}$

⠀

∴ Hence, Principal will be Rs. 4160.50

$\rule{300}{2}$

• V E R I F I C A T I O N :

◦ Interest for First Year :

$\implies\tt Interest = \dfrac{P \times R}{100} \\ \\\implies\tt Interest = \dfrac{4160.50 \times 4}{100} \\ \\\implies\tt Interest = 166.42$

◦ Interest for Second Year :

$\implies\tt Interest = \dfrac{(P+Interest \: of \:First \: Year) \times R}{100}\\ \\\implies\tt Interest = \dfrac{(4160.50+166.42) \times 4}{100}\\\\\implies\tt Interest = \dfrac{4326.92 \times 4}{100} \\ \\\implies\tt Interest = 339.49$

$\rule{300}{1}$

↠ Amount = Principal + (1st Yr + 2nd Yr) Int.

↠ 4500 = 4160.50 + 166.42 + 339.49

↠ Rs. 4500 = Rs. 4500 ⠀⠀Hence, Verified!

#answerwithquality #BAL

Answer 2

❏ Used ForMuLaS:-

➔ For Compound interest

$\sf\longrightarrow\boxed{ P_c=P(1+\frac{r}{100}){}^{n\times t}}$

$\sf\longrightarrow\boxed{I_c=P[(1+\frac{r}{100}){}^{n\times t}-1]}$

➔ For Simple interest

$\sf\longrightarrow\boxed{I_s=\frac{Prt}{100}}$

$\sf\longrightarrow\boxed{P_s=(P+\frac{Prt}{100})}$

Where ➔ • $P_c$= Total amount after

compound interest .

• $P_s$= Total amount after

Simple interest .

• P= principal amount.

• t= time.

• r= rate of interest.

• n= No. of interest cycle per year .

Ex:-

➝n=1 (when compounded annually)

➝n=2 (when compounded half yearly)

➝n=4 (when compounded quarterly)

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❏ Question:-

Q) Find the principal which will amount to 4500 in 2 years at rate of 4% per annum compounded annually.

❏ Solution:-

❚❚❚ Given:

• Time(t)= 2 years

• Interest rate(r)= 4%

• $P_c$ = 4500 Rs

• n=1 [∵ compounded only]

❚❚❚To Find:

• Principal= P (let)

➾ Now , using the above Formula of compound interest,

$\sf\longrightarrow P_c=P\times(1+\frac{r}{100}){}^{n\times t}$

$\sf\longrightarrow 4500=P\times(1+\frac{4}{100}){}^{1\times 2}$

$\sf\longrightarrow 4500=P\times(\frac{100+4}{100}){}^{1\times 2}$

$\sf\longrightarrow 4500=P\times(\frac{104}{100}){}^{2}$

$\sf\longrightarrow 4500=P\times\frac{104\times104}{100\times100}$

$\sf\longrightarrow \cancel{4500}\times\frac{100\times100}{\cancel{104}\times\cancel{104}}=P$

$\sf\longrightarrow P=(0.416050\times100\times100)$

$\sf\longrightarrow \boxed{\large{\red{P=4160.50\:Rs}}}$

∴ The principal was =4160.50 Rs

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

#answerwithquality & #BAL