Question

plz answer this maths question ​

Answer 1

Answer:

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Answer 2

Question

Calculate the amount and the compound interest on ₹17000 in three years when the rate of interest for successive years are 10%, 10% and 14% respectively.

Answer

Given :

Principle : ₹17000

Rate of interest(s) : 10%, 10% and 14%

Time : 3 years

To find :

The amount and the compound interest for the successive years.

Solution :

First, we'll find the amount and the compound interest for first year.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 17000 \bigg( 1 + \dfrac{10}{100} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( 1 + \dfrac{1}{10} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{10 + 1}{10} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{11}{10} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{11}{10} \bigg)$

$\sf \dashrightarrow \dfrac{17000 \times 11}{10} = \dfrac{187000}{10}$

$\sf \dashrightarrow \cancel \dfrac{187000}{10} = 18700$

Compound interest (first year) :

$\sf \dashrightarrow CI = Amount - Principle$

$\sf \dashrightarrow 18700 - 17000$

$\dashrightarrow$₹$\sf 1700$

As we can see that the rate of interest is same at first and second years. So, the values remains same.

Hence, the amount and compound interest for first and second year is ₹18700 and ₹1700 respectively.

Now, let's find the amount and compound interest for third year.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 17000 \bigg( 1 + \dfrac{14}{100} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( 1 + \dfrac{7}{50} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{50 + 7}{50} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{57}{50} \bigg)^{1}$

$\sf \dashrightarrow 17000 \bigg( \dfrac{57}{50} \bigg)$

$\sf \dashrightarrow \dfrac{17000 \times 57}{50} = \dfrac{969000}{50}$

$\sf \dashrightarrow \cancel \dfrac{187000}{50} = 19380$

Compound interest (first year) :

$\sf \dashrightarrow CI = Amount - Principle$

$\sf \dashrightarrow 19380 - 17000$

$\dashrightarrow$₹$\sf 2380$

Hence, the amount and compound interest for third year is ₹19380 and ₹2380 respectively.