Question

A sum amounts to * 2,970.25 in 2 years at 9% per annum, compounded annually.
Find the sum.​

Answer 1

$\bf \: \underline{Given} :$ ↴

$\sf \: Amount = Rs. \: 2970.25$

$\sf \: Rate = 9 \: \%$

$\sf \: Time = 2 \: Years$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: (Sum) \: Principal.$

$\bf \star \: \underline{So, \: Let's \: Start} \: \star$

$\sf \: We \: know \: that :$ ↴

$\ \boxed{ \pink{\sf \: Amount = P \: \bigg(1 + \dfrac{R }{100} \bigg) ^{n} }}$

$\sf \: \underline{Putting \: the \: values}$

$\sf \:2970.25 = P \: \bigg(1 + \dfrac{9 }{100} \bigg) ^{2}$

$\sf \:2970.25 = P \: \bigg(\dfrac{109 }{100} \bigg) ^{2}$

$\sf \:2970.25 = P \: \times \: \dfrac{109 }{100} \: \times \: \dfrac{109 }{100}$

$\bf \: \underline{ Now},$

$\dfrac{2970.25 \times 100 \times 100}{109 \times 109}$

$\sf \: Now, \: we \: will \: remove \: the \: decimal.$

$\dfrac{297025 \times 100 \times 100}{100 \times 109 \times 109}$

$\sf \: Now, \: we \: will \: simplify \: the \: above \: expression.$

$\dfrac{1188 \times 100 \times 100}{4\times 109 \times 109}$

$\dfrac{109\times 100 \times 100}{4\times 109 }$

$\dfrac{ 100 \times 100}{4}$

$\sf \: \dfrac{ 25 \times 100}{1} \:$

$\sf \: 25 \times 100 \: = \: 2500$

$\purple{ \sf \: So, \: our \: answer \: is \: Rs. \: 2500. }$

Answer 2

${ \red{\sf \: Amount = P \: \bigg(1 + \dfrac{R }{100} \bigg) ^{n} }} \\ \\ \sf⇛ \:2970.25 = P \: \bigg(\dfrac{109 }{100} \bigg) ^{2} \\ \\⇛ \sf \: 2970.25=p \times ( \frac{ 109 }{ 100 } ) ^ { 2 } \\ \\ \sf \: {\green{Calculate \: \frac{109}{100} \: to \: the \: power \: of \: 2 \: and \: get \: \frac{11881}{10000}}} \\ \\ ⇛ \sf \: 2970.25=p\times \left(\frac{11881}{10000}\right) \\ \\ ⇛ \sf \: p\times \left(\frac{11881}{10000}\right)=2970.25 \\ \\ \sf \: { \green{Multiply \: both \: sides \: by \: \frac{10000}{11881}, \: the \: reciprocal \: of \: \frac{11881}{10000}}} \\ \\ ⇛\sf \: p=2970.25\times \left(\frac{10000}{11881}\right) \\ \\ \sf \: { \green{Convert \: decimal \: number \: 2970.25 \: to \: fraction \: \frac{297025}{100} }} \\ \sf \:{ \green{ Reduce \: the \: fraction \: \frac{297025}{100} \: to \: lowest \: terms \: by}} \\ \sf \: { \green{ extracting \: and \: cancelling \: out \: 25}} \\ \\ ⇛\sf \: p=\frac{11881}{4}\times \left(\frac{10000}{11881}\right) \\ \\⇛ \sf \: p=\frac{11881\times 10000}{4\times 11881} \\ \\⇛ \sf \: p=\frac{10000}{4} \\ \\⇛ \sf \: p=2500 \\ \\ \\ \: \: \: \: \: \: \: \: \: \large \sf{ \red{{@WildCat7083 }}}$