Question

what is the difference between simple interest and compound interest on a sum of Rs1000,at 10%per annum after 4 years​

Answer 1

Given :-

• Principal (P) = 1000
• Rate (R) = 10%
• Time (T) = 4 year

To Find :-

Difference between simple and compound interest

Solution :-

For SI

• SI = P × R × T/100
• SI = 1000 × 10 × 4/100
• SI = 10 × 10 × 4
• SI = 400

For CI

• CI = P(1 + r/100)ⁿ - [P]
• CI = 1000(1 + 10/100)⁴ - 1000
• CI = 1000(100 + 10/100)⁴ - 1000
• CI = 1000(110/100)⁴ - 1000
• CI = 1000(1.4641) - 1000
• CI = 1464.1 - 1000
• CI = 464.1

Difference

• CI - SI
• 464.1 - 400
• 64.1

Answer 2

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

Case - 1 Simple Interest

Given that,

↝ Sum invested, p = Rs 1000

↝ Rate of interest, r = 10 % per annum

↝ Time period, n = 4 years

We know,

Simple interest (S.I.) on a certain sum of money of Rs p invested at the rate of r % per annum for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: S.I \: = \: \frac{p \times r \times n}{100} \: }}$

So, on substituting the values, we get

$\rm :\longmapsto\:S.I \: = \: \dfrac{1000 \times 10 \times 4}{100}$

$\rm \implies\:\boxed{ \tt{ \: S.I \: = \:Rs \: 400 \: }} - - - (1)$

Case - 2 Compound interest

Given that,

↝ Sum invested, p = Rs 1000

↝ Rate of interest, r = 10 % per annum compounded annually

↝ Time period, n = 4 years

We know,

Compound interest (C.I.) on a certain sum of money of Rs p invested at the rate of r % per annum compounded annually for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: C.I. \: = \: p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} - p}}$

So, on substituting the values, we get

$\rm :\longmapsto\:\: C.I. \: = \: 1000 {\bigg[1 + \dfrac{10}{100} \bigg]}^{4} - 1000$

$\rm :\longmapsto\:\: C.I. \: = \: 1000 {\bigg[1 + \dfrac{1}{10} \bigg]}^{4} - 1000$

$\rm :\longmapsto\:\: C.I. \: = \: 1000 {\bigg[ \dfrac{10 + 1}{10} \bigg]}^{4} - 1000$

$\rm :\longmapsto\:\: C.I. \: = \: 1000 {\bigg[ \dfrac{14641}{10000} \bigg]}- 1000$

$\rm :\longmapsto\:\: C.I. \: = \: {\bigg[ \dfrac{14641}{10} \bigg]}- 1000$

$\rm :\longmapsto\:\: C.I. \: = \: 1464.10- 1000$

$\rm \implies\:\boxed{ \tt{ \: C.I. \: = \: Rs \: 464.10 \: }} - - - (2)$

Hence,

$\red{\rm :\longmapsto\:C.I. \: - \: S.I \: }$

$\rm \:  =  \:464.10 - 400$

$\rm \:  =  \:64.10$

Therefore,

$\rm \implies\:\boxed{ \tt{ \: C.I. - S.I \: = Rs \: 64.10 \: }}$

More to know :-

1. Compound interest (C.I.) on a certain sum of money of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: C.I. \: = \: p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} - p}}$

2. Compound interest (C.I.) on a certain sum of money of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: C.I. \: = \: p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} - p}}$

3. Compound interest (C.I.) on a certain sum of money of Rs p invested at the rate of r % per annum compounded monthly for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: C.I. \: = \: p {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} - p}}$