Question

In the following cases, find the amount and compound interest ( interest compound annually). 1. principal = 45000, rate p.a. = 5%, time = 3years​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Principal, P = 45000

Rate, r = 5 % per annum

Time, n = 3 years

We know,

Amount on a certain sum of money of P invested at the rate of r % per annum compounded annually for n years is given by

$\boxed{\sf{  \: \: Amount \: = \: P\bigg[1 + \dfrac{r}{100} \bigg]^{n} \: \: }}$

So, on substituting the values, we get

$\rm \: Amount \: = \: 45000 {\bigg[1 + \dfrac{5}{100} \bigg]}^{3}$

$\rm \: Amount \: = \: 45000 {\bigg[1 + \dfrac{1}{20} \bigg]}^{3}$

$\rm \: Amount \: = \: 45000 {\bigg[\dfrac{20 + 1}{20} \bigg]}^{3}$

$\rm \: Amount \: = \: 45000 {\bigg[\dfrac{21}{20} \bigg]}^{3}$

$\rm \: Amount \: = \: 45000 \: \times \: \dfrac{9261}{8000}$

$\rm \: Amount \: = \: 45 \: \times \: \dfrac{9261}{8}$

$\rm\implies \:Amount \: = \: 52093.12 \:$

Now, we know that

Compound interest is evaluated as

$\rm \: Compound\:interest = Amount - Principal$

$\rm \: =  \: \: \: 52093.12 - 45000$

$\rm \: =  \: \: \: 7093.12$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{Amount = 52093.12} \\ \\ &\sf{Compound\:interest = 7093.12} \end{cases}\end{gathered}\end{gathered}$

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Additional Information:-

1. Amount on a certain sum of money of P invested at the rate of r % per annum compounded semi - annually for n years is given by

$\boxed{\sf{  \: \: Amount \: = \: P\bigg[1 + \dfrac{r}{200} \bigg]^{2n} \: \: }}$

2. Amount on a certain sum of money of P invested at the rate of r % per annum compounded quarterly for n years is given by

$\boxed{\sf{  \: \: Amount \: = \: P\bigg[1 + \dfrac{r}{400} \bigg]^{4n} \: \: }}$

3. Amount on a certain sum of money of P invested at the rate of r % per annum compounded monthly for n years is given by

$\boxed{\sf{  \: \: Amount \: = \: P\bigg[1 + \dfrac{r}{1200} \bigg]^{12n} \: \: }}$

Answer 2

Given :-

• Principal = Rs. 45,000
• Rate = 5% p.a
• Time = 3 y

To Find :-

Amount

CI

Solution :-

We know that

A = P(1 + r/100)ⁿ

A = 45000(1 + 5/100)³

A = 45000(100 + 5/100)³

A = 45000(105/100)³

A = 45000(21/20)

A = 45000 × 9261/8000

A = 45 × 9261/8

A = 4,16,745/8

A = 52093.12

Now

CI = A - P

CI = 52093.12 - 45000

CI = Rs. 7093.12