Question

p=1000 r=2% t=2 years find amount at compounded annually and compunded half yearly​

Answer 1

GivEn :-

• P = 1000
• R = 2%
• t = 2 years

To Find :-

• amount at compounded annually
• and compounded half yearly

Step-by-step explanation:

➤ Amount at compounded annually :-

$\boxed{ \sf{A_{annually} = P (1 +\dfrac{R}{100} )^{n} }}$

• P = Principal
• r = Rate of interest
• n = Time

➤ Substituting the values,

$\implies \sf{A_{annually} = 1000(1 +\dfrac{2}{100} )^{2} }$

$\implies \sf{A_{annually} = 1000 \times {(\dfrac{102}{100} )}^{2} }$

$\implies \sf{A_{annually} = 1000 \times \dfrac{10404}{10000} }$

$\implies \sf{A_{annually} = \dfrac{10404}{10} }$

$\implies \boxed{ \red{ \bold{{A_{annually} = 1040.4}}}}$

➤ Amount at compounded half yearly :-

$\boxed{ \sf{A_{half \: yearly} = P (1 +\dfrac{R}{200} )^{2n} }}$

➤ Substituting the values,

$\implies \sf{A_{half \: yearly} = 1000 \times {(1 + \dfrac{100}{200} )}^{2 \times 2} }$

$\implies \sf{A_{half \: yearly} = 1000 \times {(1 + \dfrac{1}{2} )}^{4} }$

$\implies \sf{A_{half \: yearly} = 1000 \times {(\dfrac{3}{2} )}^{4} }$

$\implies \sf{A_{half \: yearly} = 1000 \times {\dfrac{81}{16}}}$

$\implies \sf{A_{half \: yearly} ={\dfrac{81000}{16}}}$

$\implies \boxed{ \red{ \bold{ {A_{half \: yearly} =5062.5}}}}$

Answer 2

Given:-

➯Principal = 1000

➯Rate of Interest = 2 %

➯Time = 2 Years

To Find:-

➯Amount at compounded Annually

➯Amount at compounded Half yearly

Solution:-

➊First Case:-

✦To Find the amount compounded at Annually,

➯Using formula,

➯Let time be n

$\longmapsto \: \: \bigstar \: { \underline{ \boxed{ \sf{ \red{Aannually \: amount \: compounded = P (1 + \frac{R}{100}) {}^{n} }}}}} \: \bigstar$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded = 1000 (1 + \frac{2}{100}) {}^{2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded = 1000 \: ( \frac{1 \times 100}{1 \times 100} + \frac{2}{100}) {}^{2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded = 1000 \: ( \frac{100}{100} + \frac{2}{100}) {}^{2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded = 1000 \: ( + \frac{102}{100}) {}^{2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded = 1000 \: + \frac{10404}{10000}}}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Aannually \: amount \: compounded =\frac{10404}{10}}}}}$

$</strong><strong> \longmapsto \: \: \bigstar \: { \underline</strong><strong>{</strong><strong>\</strong><strong>boxed</strong><strong>{ \boxed{ \sf{ \red{Aannually \: amount \: compounded = </strong><strong>R</strong><strong>s</strong><strong>.</strong><strong>1040.4}}</strong><strong>}</strong><strong>}}} \: \bigstar$

➋Second Case:-

✦To Find The amount compounded at half Annually,

➯Using formula,

➯Let time be 2n

$\longmapsto \: \: \bigstar \: { \underline{ \boxed{ \sf{ \red{Half \: Aannually \: amount \: compounded = P (1 + \frac{R}{200}) {}^{2n} }}}}} \: \bigstar$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: (1 + \frac{2}{200}) {}^{2n} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: (1 + \frac{1}{100}) {}^{2 \times 2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: ( \frac{1 \times 100}{1 \times 100} + \frac{1}{100}) {}^{2 \times 2} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: ( \frac{100}{ 100} + \frac{1}{100}) {}^{4} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: ( \frac{101}{ 100} ) {}^{4} }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = 1000 \: ( \frac{104,060,401}{100,000,000} ) }}}}$

$\longmapsto \: \: { \underline{ \boxed{ \sf{Half \: Aannually \: amount \: compounded = \frac{104,060,401}{100,000} }}}}$

$\longmapsto \: \: \bigstar \: { \underline{ \boxed{\boxed{ \sf{ \red{Half \: Aannually \: amount \: compounded = Rs.1040.6}}}}}} \: \bigstar$

Hence,

✦The amount compounded Annually

= ₹ 1040.4

✦The amount compounded Half Annually

= ₹ 1040.6