Question

Ritika borrowed Rs 26400 from a bank to buy a TV at the rate of 15% p. a. compounded yearly. What amount will pay at the end of 2 years and 4 month.​

Answer 1

Solution:-

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$\large\to{\underbrace{\underline{\sf{Understanding\:the\:concept:-}}}}$

Here, first we will find the amount of 2 years by using the Compound Interest formula and then by calculating the Simple Interest for 4 months on the amount obtained at the end of 2 years and then we will add both of them to find the total amount to be paid after 2 years 4 months.

ANSWER:-

• The to be paid after 2 years and 4 months is Rs.36659.7

GIVEN:-

• Principal = Rs 26400
• Rate = 15%
• Time = 2 Years and 4 Months

TO FIND:-

• Total amount to be paid after 2 years 4 months = ?

FORMULA:-

$\begin{gathered}\dashrightarrow\frak{\large{Given}}=\begin{cases}&\sf{Amount=P\bigg(1+\dfrac{R}{100}\bigg)^{n}} \\\\\ &\sf{Simple \:Interest\:=\dfrac{P\times R\times T}{100}}\end{cases}\end{gathered}$

SOLVING BY APPLYING THE FORMULA:-

• Finding amount by using the formula:-

$\to\sf{Amount=P\bigg(1+\dfrac{R}{100}\bigg)^{n}}$

$\mapsto\sf{Amount=26400\bigg(1+\dfrac{15}{100}\bigg)^{2}}$

$\mapsto\sf{Take \ LCM}$

$\mapsto\sf{Amount=26400\bigg(\dfrac{100 + 15}{100}\bigg)^{2}}$

$\mapsto\sf{Amount=26400\bigg(\dfrac{115}{100}\bigg)^{2}}$

$\mapsto\sf{Amount=26400\bigg(\dfrac{13225}{10000}\bigg)}$

$\mapsto\sf{Amount=26400\times\dfrac{13225}{10000}}$

$\mapsto\sf{Amount=\dfrac{26400 \times 13225}{10000}}$

$\mapsto\sf{Amount=\dfrac{349140000}{10000}}$

$\mapsto\sf{Cancle \: the \: zeros}$

$\mapsto\sf{Amount=\dfrac{34914}{1}}$

$\mapsto\sf{Amount= Rs.34914}$

Hence, the amount of two years is Rs.34914.

• Finding the simple interest by using the formula:-
• Here, we will consider the amount of 2 years as the principal.

$\mapsto\sf{Simple\:Interest = \dfrac{P \times R \times T}{100} }$

$\mapsto\sf{Simple\:Interest = \dfrac{34914 \times 15 \times \frac{1}{3} }{100} }$

$\mapsto\sf{Simple\:Interest = \dfrac{34914 \times 60}{100} }$

$\mapsto\sf{Simple\:Interest = \dfrac{2094840}{100}}$

$\mapsto\sf{Simple\:Interest = \dfrac{2094840}{100}} = 1745.7$

$\mapsto\sf{Simple\:Interest = Rs.1745.7}$

Hence, the Simple Interest of four months is Rs.1745.7.

• Amount to be paid in 2 years and 4 months = Amount + Simple Interest
• Amount = Rs 34914
• Simple Interest = Rs 1745.7
• Total Amount to be paid = Rs 34914 + Rs 1745.7
• Total Amount to be paid = 34914 + 1745.7 = 36659.7
• Total Amount to be paid = Rs 36659.7

Hence, the to be paid after 2 years and 4 years is Rs.36659.7

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