Question

Find the compound interest, if the amount of a certain principal after 2 years is ₹ 4036.80 at a rate of 16 p.cp.a *
1 point
₹ 3000
₹ 1035.80
₹ 1036.80
₹ 1020.00​

Answer 1

$\underline{ \underline{ \Large \pmb{\mathit{ {Given:}} }} }$

• Amount (A) = ₹ 4036.80

• Rate (R) = 16 % p.a

• Time (n years) = 2 years

$\underline{ \underline{ \Large \pmb{\mathit{ {To \: calculate:}} }} }$

• Compound Interest (C.I)

$\underline{ \underline{ \Large \pmb{\mathit{ {Calculation:}} }} }$

As we know that,

$\bigstar \: \boxed{\sf {C.I = Amount - Principal}}$

We aren't given the Principal, let's calculate the Principal first.

As we know that,

$\bigstar \: \boxed{\sf {A = {P \Bigg \lgroup 1 + \dfrac{R}{100} \Bigg \rgroup}^{n} }}$

Where,

• P = Principal

• A = Amount

• n = number of years/time

• R = Rate

$\longrightarrow \sf {4036.80 = {P \Bigg \lgroup 1 + \dfrac{16}{100} \Bigg \rgroup}^{2}}$

$\longrightarrow \sf {4036.80 = {P \Bigg \lgroup \dfrac{100 +16}{100} \Bigg \rgroup}^{2}}$

$\longrightarrow \sf {4036.80 = {P \Bigg \lgroup \dfrac{116}{100} \Bigg \rgroup}^{2}}$

$\longrightarrow \sf {4036.80 = P \times \dfrac{116}{100} \times \dfrac{116}{100} }$

$\longrightarrow \sf {4036.80 \times \dfrac{116}{100} \times \dfrac{100}{116} = P}$

$\longrightarrow \sf { \dfrac{403680}{\cancel{100}} \times \dfrac{\cancel{100}}{116} \times \dfrac{100}{116} =P }$

$\longrightarrow \sf {403680 \times \dfrac{1}{116} \times \dfrac{100}{116} = P }$

$\longrightarrow \sf { \dfrac{403680 \times 1 \times 100}{116 \times 116} = P }$

$\longrightarrow \sf { \dfrac{\cancel{403680} \times 1 \times 100}{\cancel{116} \times 116} = P }$

$\longrightarrow \sf { \dfrac{3480 \times 1 \times 100}{116} = P }$

( Cancel 3480 in numerator and 116 in denominator by 4)

$\longrightarrow \sf { \dfrac{ \cancel{870} \times 1 \times 100}{\cancel{29}} = P }$

$\longrightarrow \sf { 30 \times 1 \times 100= P }$

$\longrightarrow \sf { 30 \times 100= P }$

$\longrightarrow \boxed{ \sf { Rs. \: 3000= P }}$

Therefore, principal us Rs. 3000. Now, substitute the values in the formula of C.I to find the compound interest.

$\bigstar \: \boxed{\sf {C.I = Amount - Principal}}$

$\longrightarrow \sf {C.I =Rs. \: 4036.80 - 3000}$

$\longrightarrow \boxed { \pmb {\rm \red {C.I =Rs. \: 1036.80 } }}$

Therefore, C.I is ₹ 1036.80 and Option C is correct.