Question

Anamika deposited Rs. 24000 at 10% annual interest for 1 1/2 years. If the interest is calculated every 6 months, how much money will she get on maturity?

Rs. 28657

Rs. 27783

Rs. 34256

Rs. 25678​

which one is the answer?

Answer 1

2nd option

Amount = Rs. 27783

Solution :-

Given that

The amount deposited by Anamika = Rs. 24000

Rate of interest = 10%

Time = 1 1/2 years = 3/2 years

The interest is calculated for ever 6 months then

Number of times the interest is calculated for 3/2 years = 3

Rate of interest for 6 months = 10/2 = 5%

We know that

Amount = P[1+(R/100)]^n

=> A = 24000[1+(5/100)]³

=> A = 24000[1+(1/20)]³

=> A = 24000[(20+1)/20]³

=> A = 24000(21/20)³

=> A = 24000×(21×21×21)/(20×20×20)

=> A = 24×21×21×21/8

=> A = 3×21×21×21

=> A = 27783

Therefore, Amount = Rs. 27,783

Answer:-

She will get Rs. 27,783 on time of maturity .

Used formulae:-

→ Amount = P[1+(R/100)]^n

• A = Amount
• P = Principal
• R = Rate of Interest
• n = Number of times the interest calculated compoundly

Answer 2

Given :

• Principal = Rs.24000
• Rate = 10 %
• Time = 1.5 years

To Find : Find the Amount of Maturity

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

$\qquad \; {\red{\bigstar \; {\purple{\underbrace{\underline{\orange{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup ^{2n} }}}}}}}}$

Where :

• A = Amount
• P = Principal
• R = Rate
• n = Time

$\dag$ Calculating the Amount of Maturity :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup ^{2n} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + \dfrac{10}{200} \bigg\rgroup ^{2 \times 1.5} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + \dfrac{10}{100} \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + \cancel\dfrac{10}{200} \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + \dfrac{5}{100} \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + \cancel\dfrac{5}{100} \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1 + 0.05 \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \bigg\lgroup 1.05 \bigg\rgroup ^{3} } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \times 1.05 \times 1.05 \times 1.05 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { A = 24000 \times 1.157625 } \\ \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ Amount = Rs. \; 27783 }}}}} \; {\pink{\pmb{\bigstar}}} \\ \\ \\ \\ \end{gathered}$

$\therefore \;$ Anamika will Receive Rs. 27783 at the time of Maturity .

$\\ \qquad{\rule{200pt}{2pt}}$