Question

If rahul has taken a loan of 5000Rs at a rate of 8 pcpa for 3 yrs. If the interest is compounded annually then how many rupees should he pay to clear his loan? ​

Answer 1

Answer:

• Rahul has to pay ₹ 6298.56.

Step-by-step explanation:

Given that:

• Rahul has taken a loan of ₹ 5000, at a rate of 8% p.c.p.a. for 3 years.
• The interest is compounded annually.

To Find:

• Amount that should be payed by Rahul to clear his loan.

Formula Used:

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

Where,

• Principal = ₹ 5000
• Rate = 8%
• Time = 3 years

Substituting the values,

$\sf{Amount=5000\bigg(1+\dfrac{8}{100}\bigg)^{3}}$

Adding 1 and 8/100,

$\sf{\longrightarrow 5000\bigg(\dfrac{100+8}{100}\bigg)^{3}}\\\\\sf{\longrightarrow 5000\bigg(\dfrac{108}{100}\bigg)^{3}}$

Opening the bracket,

$\sf{\longrightarrow 5000 \times\dfrac{108}{100}\times\dfrac{108}{100}\times\dfrac{108}{100}}$

Cutting the zeros,

$\sf{\longrightarrow 5\!\!\!\not{0}\!\!\!\not{0}\!\!\!\not{0} \times\dfrac{108}{1\!\!\!\not{0}\!\!\!\not{0}}\times\dfrac{108}{10\!\!\!\not{0}}\times\dfrac{108}{100}}\\\\\sf{\longrightarrow 5\times\dfrac{108}{1}\times\dfrac{108}{10}\times\dfrac{108}{100}}$

Multiplying the numbers,

$\sf{\longrightarrow \dfrac{62,98,560}{1000}}\\\\\longrightarrow\dfrac{629856\!\!\!\not{0}}{100\!\!\!\not{0}}\\\\\longrightarrow\dfrac{629856}{100}$

Dividing the numbers,

$\sf{\longrightarrow 6298.56}$

Hence, Rahul has to pay ₹ 6298.56 to clear his loan.