Question

Find the compound interest if the amount of a certain principal after two years

is `4036.80 at the rate of 16 p.c.p.a.​

Answer 1

Question :-

• Find the compound interest if the amount of a certain principal after two years is 4036.80 at the rate of 16 p.c.p.a.

Answer :-

• Compound interest is equal to 1036.8/0 rupees.

Given :-

• Amount = 4036.80
• Rate = 16%
• Time = 2 years

To find :-

• Compound interest.

Step by step explanation :-

We know Amount, Rate and time I.e 4036.80 , 16% and 2 years.

We are asked to find compound interest.

We need to know the principal, So that we can find compound interest.

To find principal, We will use the formula given below :-

$\boxed{ \mathfrak{A = P \bigg[ 1 +{ \dfrac{Rate}{100}}^{Time}\bigg]}}$

Applying this,

$\implies \sf 4036.80 = P{\bigg[ 1 + \frac{16}{100} \bigg] }^{2}$

Dividing 16 by 100,

$\implies \sf 4036.80 = P{\bigg[ 1 + 0.16\bigg] }^{2}$

$\implies \sf 4036.80 = P{\bigg[ 1.16\bigg] }^{2}$

As P is a variable, And we know that variables should always be at left side. So, Transposing P from RHS to LHS and 4036.80 from LHS to RHS.

$\implies \sf 4036.80 = P{\bigg[ 1.16\bigg] }^{2}$

$\implies \sf P = \dfrac{4036.80}{ {1.16}^{2} }$

$\implies \sf P = \bigg( \dfrac{ 4036.80}{ 1.3456 } \bigg)$

Dividing this,

$\implies \sf P = 3000$

Thus, Principal = 3000 Rupees.

Now, To find compound interest, We will use the formula given below :-

$\boxed{ \mathfrak{Compound \: interest = Amount - Principal }}$

Applying this,

$\implies \sf C.I = 4036.80 - 3000$

$\implies \sf C.I = 1036.80$

Therefore, Compound interest is equal to 1036.80 rupees.

Answer 2

AnswEr-:

• $\dag{\underline {\red{\mathrm {\bf {Compound\:Interest= Rs.1036.80 }}}}}$

Explanation -:

$\mathrm {\bf { Given-:}}$

• Amount = Rs . 4036.80
• Rate = 16 % p.a
• Time = 2 yrs

$\mathrm {\bf { To|:Find-:}}$

• Compound Interest

$\dag {\mathrm {\bf { Solution \:of\:Question-:}}}$

• $\underbrace{\mathrm { Understanding \: the \: Concept-:}}$

• We have to find the Compound Interest when Amount, Rate and Time is Given.

• First we have to find the Principal by Putting known Values in the Formula for Amount.

• Then ,

• By Putting Principal and Amount in the Formula for Compound Interest,

• We can get the Compound Interest.

As , We know that ,

• $\underline {\boxed {\mathrm {\pink{ Amount = Principal \left( 1 + \dfrac{Rate}{100} \right)^{Time} }}}}$

$\mathrm {\bf { Here-:}}$

• Amount = Rs . 4036.80
• Rate = 16 % p.a
• Time = 2 yrs

Now By Putting known Values in Formula for Amount-:

• $\longmapsto { \mathrm {\bf{ Rs.4036.80 = Principal \left( 1 + \dfrac{16}{100} \right)^{2}}}}$

• $\longmapsto { \mathrm {\bf{ Rs.4036.80 = Principal \left( 1 + 0.16 \right)^{2}}}}$

• $\longmapsto { \mathrm {\bf{ Rs.4036.80 = Principal \left( 1.3456 \right)}}}$

• $\longmapsto { \mathrm {\bf{ \dfrac{4036.80}{1.3456} = Principal }}}$

• $\longmapsto { \mathrm {\bf{ \dfrac {\cancel {4036.80}}{\cancel{1.3456}} = Principal }}}$

• $\underline{\boxed { \mathrm {\bf{ Rs.3000 = Principal }}}}$

Therefore,

• $\underline{\dag { \mathrm {\bf{ Rs.3000 = Principal }}}}$

___________________________________

As , We know that,

• $\underline {\boxed {\mathrm {\pink{ Compound \:Interest\:= Amount - Principal }}}}$

$\mathrm {\bf { Here-:}}$

• $\longmapsto { \mathrm {\bf{ Rs.3000 = Principal }}}$

• $\longmapsto { \mathrm {\bf{ Rs.4036.80 = Amount}}}$

Now By Putting known Values in Formula for Compound Interest-:

• $\longmapsto { \mathrm {\bf{Compound\:Interest= 4036.80 -3000 }}}$

• $\underline {\boxed{ \mathrm {\bf{Compound\:Interest= Rs.1036.80 }}}}$

Hence ,

• $\dag{\underline {\red{\mathrm {\bf {Compound\:Interest= Rs.1036.80 }}}}}$

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