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Leila aspires to buy a car worth $Rs. 10,00,000$ after $5$ years. What is the minimum amount in Rupees that she should deposit now in a bank which offers $10\%$ annual rate of interest, if the interest was compounded annually?

1. $5,00,000$
2. $6,21,000$
3. $6,66,667$
4. $7,50,000$

Let's assume the principal amount be $P.$

After getting an annual rate of interest as $10\%$ which is compounded annually, $5$ years later the amount should be $10,00,000$

So, $P\left(1 + \dfrac{10}{100}\right)^5 = 10,00,000$

$\quad \implies P\left(\dfrac{11}{10}\right)^5 = 10^6$

$\quad \implies P = \dfrac{10^6 * 10^5}{(11)^5} = \dfrac{10 ^ {11}}{11^5}$

$\quad P = 620921.323 \approx 621000$

Option (B)

Compound interest : $A=P\left ( 1+\dfrac{R}{100} \right )^T$

$\underbrace{|......10.....|......10......|......10.....|......10.....|......10.....|}$

$5 \ years$

$10,00,000=P\left ( 1+\dfrac{10}{100} \right )^5=$ $620921.32=6,21,000$