Question

Calculate the amount and the compound interest on rs 5000 in 2 years when the rate of interest for successive years is 6% and 8% respectively.​

Answer 1

Given :

• Principal (P) = Rs. 5000

• Time (n) = 2 years

• Rate ($\sf {R_1}$ ) = 6%

• Rate ($\sf {R_2}$ ) = 8%

To calculate :

• Amount (A)

• Compound interest (CI)

Calculation :

We know that, when the rates of interest for 2 years are different then Amount is :

$\bigstar \: \boxed{\sf {A = P \Bigg \lgroup 1 + \dfrac{R_1}{100} \Bigg \rgroup \Bigg \lgroup 1 + \dfrac{R_2}{100} \Bigg \rgroup }}$

$\longrightarrow \sf { A =Rs. \: 5000 \Bigg \lgroup 1 + \dfrac{6}{100} \Bigg \rgroup \Bigg \lgroup 1 + \dfrac{8}{100} \Bigg \rgroup }$

$\longrightarrow \sf { A = Rs. \: 5000 \Bigg \lgroup 1 + \dfrac{3}{50} \Bigg \rgroup \Bigg \lgroup 1 + \dfrac{4}{50} \Bigg \rgroup }$

$\longrightarrow \sf { A = Rs. \: 5000 \Bigg \lgroup \dfrac{50 + 3}{50} \Bigg \rgroup \Bigg \lgroup \dfrac{50+4}{50} \Bigg \rgroup }$

$\longrightarrow \sf { A = Rs. \: 5000 \Bigg \lgroup \dfrac{53}{50} \Bigg \rgroup \Bigg \lgroup \dfrac{54}{50} \Bigg \rgroup }$

$\longrightarrow \sf { A = Rs. \: 5000 \times \dfrac{53}{50} \times \dfrac{54}{50} }$

$\longrightarrow \sf { A = Rs. \: 50 \times \dfrac{53}{5} \times \dfrac{54}{5} }$

$\longrightarrow \sf { A =Rs. \: 10 \times \dfrac{53}{5} \times 54 }$

$\longrightarrow \sf { A = Rs. \: 2 \times 53 \times 54 }$

$\longrightarrow \sf \red { Amount = Rs. \: 5724 }$

Also, we know that :

$\bigstar \: \boxed{\sf {CI = Amount - Principal}}$

$\longrightarrow \sf {CI = Rs. \: ( 5724 - 5000) }$

$\longrightarrow \sf \red { CI = Rs. \: 724 }$

Therefore,

• Amount is Rs. 5724.
• Compound interest is Rs. 724.