Question

At what rate per cent per annum will ₹4800 yield an interest of ₹747 in 2 years compounded annually ?​

Answer 1

Answer:

Given :-

• A sum of money is ₹4800 yield an interest of ₹747 in 2 years compounded annually.

To Find :-

• What is the rate of interest per annum.

Formula Used :-

$\clubsuit$ Amount Formula :

$\mapsto \sf\boxed{\bold{\pink{Amount =\: Principal + Interest}}}$

$\clubsuit$ Compound Interest or C.I in annually Formula :

$\mapsto \sf\boxed{\bold{\pink{A =\: P\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup^n}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time

Solution :-

First, we have to find the amount :

Given :

• Principal = ₹4800
• Interest = ₹747

According to the question by using the formula we get,

➦ Amount = ₹4800 + ₹747

➦ Amount = ₹5547

Now, we have to find the rate of interest :

Let,

$\mapsto \bf Rate\: of\: Interest =\: r\%$

Given :

• Amount (A) = ₹5547
• Principal (P) = ₹4800
• Time (n) = 2 years

According to the question by using the formula we get,

$\longrightarrow \sf 5547 =\: 4800\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup^2$

$\longrightarrow \sf 5547 =\: 4800\bigg\lgroup \dfrac{100 + r}{100}\bigg\rgroup^2$

$\longrightarrow \sf \dfrac{\cancel{5547}}{\cancel{4800}} =\: \bigg\lgroup \dfrac{100 + r}{100}\bigg\rgroup^2$

$\longrightarrow \sf \dfrac{1849}{1600} =\: \bigg\lgroup \dfrac{100 + r}{100}\bigg\rgroup^2$

$\longrightarrow \sf \bigg\lgroup \dfrac{43}{40}\bigg\rgroup^2 =\: \bigg\lgroup \dfrac{100 + r}{100}\bigg\rgroup^2$

$\longrightarrow \sf \dfrac{43}{40} =\: \dfrac{100 + r}{100}$

By doing cross multiplication we get,

$\longrightarrow \sf 40(100 + r) =\: 43(100)$

$\longrightarrow \sf 4000 + 40r =\: 4300$

$\longrightarrow \sf 40r =\: 4300 - 4000$

$\longrightarrow \sf 40r =\: 300$

$\longrightarrow \sf r =\: \dfrac{30\cancel{0}}{4\cancel{0}}$

$\longrightarrow \sf r =\: \dfrac{30}{4}$

$\longrightarrow \sf\bold{\red{r =\: 7.5\%}}$

${\small{\bold{\underline{\therefore\: The\: rate\: of\: interest\: per\: annum\: is\: 7.5\%\: .}}}}$

Answer 2

Given :

• At what rate per cent per annum will ₹4800 yield an interest of ₹747 in 2 years compounded annually ?

To Find :

• rate of interest per annum.

Formula :

$\longrightarrow \sf\boxed{\bold{\blue{Amount =\: Principal + Interest}}}$

Solution :

$\tt\sf\red\rightarrow \: \red{Principal =₹4800 }$

$\tt\sf\pink\rightarrow \: \pink{Interset =₹747 }$

$\tt\sf\rightarrow \: {Amount= Principal+Interest }$

$\tt\sf\green\rightarrow \: \green{4800+747 }$

$\tt\sf\green\rightarrow \: \red{5547 }$

$\tt\sf\blue\rightarrow \: \blue{Time=2 years }$

$\tt\sf\orange\rightarrow \: \orange{No. \: of \: compound \: per \: year=1 }$

$\tt\sf\ \: {Let \: the \: rate \: of \: interest \: be \: r \: precentage }$

$\dashrightarrow\sf\boxed{\bold{{A =\: P\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup^t}}}$

$\dashrightarrow\sf\boxed{\bold{\green{5547 =4800\bigg\lgroup 1 + \dfrac{r}{100}\bigg\rgroup^2}}}$

$\tt\sf\red\rightarrow \: \red{7.5 \: percentage }$

Hence

• The final answer is 7.5 % .