Question

Find the amount and compound interest payable annually on Rs16000 for 2 years at 15% and

12% for the successive years.​

Answer 1

Answer:

• Amount = ₹20,608
• Compound interest = ₹4,608

Explanation:

Question says that,

A sum of ₹16,000 is to be compound annually for 2 successive years at the rate of 15% and 12% respectively.

Find the amount and the compound interest.

Using the formula :

$\sf \longrightarrow Amount = p \bigg(1 + \dfrac{r_1}{100} { \bigg)} \times \bigg( 1 + \dfrac{r_2}{100} \bigg)$

Where,

• ‘p’(principal) = 16,000
• $\sf r_1$ (rate for the first year) : 15%
• $\sf r_2$ (rate for the second year) : 12%

So, the amount is :

$\sf \longrightarrow 16000\bigg(1 + \dfrac{15}{100} { \bigg)} \times \bigg( 1 + \dfrac{12}{100} \bigg)$

$\sf \longrightarrow 16000 \bigg(1 + \frac{3}{20} \bigg) \times \bigg(1 + \frac{3}{25} \bigg)$

$\sf \longrightarrow 16000 \times \frac{23}{20} \times \frac{28}{25}$

$\sf \longrightarrow 32 \times 23 \times 28$

$\sf \longrightarrow 20608$

Therefore,the amount is ₹20,608

So, the compound interest is :

→ C. I. = Amount - principal

→ C. I. = 20,608 - 16,000

→ C. I. = ₹4,608

Hence, the compound interest is ₹4,608.

Answer 2

$\sf\large\underline\green{Given:-}$

$\sf{\implies Sum\:_{(money)}= \: Rs \: 16000}$

$\sf{\implies Time\:_{(annually)}=2\: years}$

$\sf{\implies Rate\:_{(interest=r_1)}=15\% \: for \: {1}^{st } \: year }$

$\sf{\implies Rate\:_{(interest=r_2)}=12\% \: for \: {2}^{nd} \: year}$

$\sf\large\underline\purple{To\: Find:-}$

$\sf{\implies Amount\:_{(after\:2\: years)}=?}$

$\sf{\implies Interest\:_{(after\:2\: years)}=?}$

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

We know,

• Amount is given by

$\boxed{ \pink{\rm \longrightarrow Amount = P \bigg(1 + \dfrac{r_1}{100} { \bigg)} ^{t_1} \times \bigg( 1 + \dfrac{r_2}{100} \bigg) ^{t_2} }}$

Where,

$\bullet \: \blue{ \sf \: P \: represents \: Principal }$

$\bullet \: \blue{\sf r_1 \: represents \:  rate \: for \: the \: t_1 \: years}$

$\bullet \: \blue{\sf r_2 \: represents \:  rate \: for \: the \: t_2 \: years}$

and

• Interest is given by

$\longrightarrow \: \large \boxed{ \green{ \rm \: Interest = Amount - Principal }}$

$\large\underline\purple{\bold{Solution :- }}$

Given that

$\bullet \: \blue{ \rm \: Principal \: = \: Rs \: 16000}$

$\bullet \: \blue{\sf r_1 \: = rate \: for \: the \: first \: year = 15\%}$

$\bullet \: \blue{\sf r_2 \: = rate \: for \: the \: second \: year = 12\%}$

So,

Amount is evaluated by using the formula, we get

$\rm :\implies\:Amount = P \bigg(1 + \dfrac{r_1}{100} { \bigg)} \times \bigg( 1 + \dfrac{r_2}{100} \bigg)$

$\rm :\implies\:Amount = 16000 \bigg(1 + \dfrac{15}{100} { \bigg)} \times \bigg( 1 + \dfrac{12}{100} \bigg)$

$\rm :\implies\:Amount = 16000 \bigg( \dfrac{115}{100} { \bigg)} \times \bigg( \dfrac{112}{100} \bigg)$

$\rm :\implies\:Amount = 16000 \times \bigg(1.15{ \bigg)} \times \bigg( 1.12 \bigg)$

$\large \boxed{ \blue{\rm :\implies\:Amount = Rs \: 20608}}$

Now,

Its Interest is evaluated using,

$\boxed{ \implies \: \green{ \rm \: Interest = Amount - Principal }}$

$\rm :\implies\:Interest \: = 20608 - 16000$

$\large{\boxed{ \implies \green{ \rm \: Interest = Rs \: 4608}}}$