GATE ECE 2018 | GA | Question: 6

Question

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?

• A. $5,00,000$
• B. $6,21,000$
• C. $6,66,667$
• D. $7,50,000$

Answer 1

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)

Answer 2

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

 

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

                                                    $5 \ years$

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

Answer 3

We don't know the principal amount

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

      $P(\dfrac{11}{10})^5$ = $10^6$

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

      $P$ = $\dfrac{10 ^ {11}}{11^5}$

      $P$ = 620921.323 ≅ 621000 Option B)