Question

mrs nalini shetty borrowed rs 26400 from a bank to buy a scooter at the rate of 15 p.c.p.a compounded anually what amount she will pay at end of 2 years 4months to clear the loan​?

Answer 1

Answer:

• Mrs. Nalini Shetty has to pay ₹ 36,659.7

Step-by-step explanation:

Given that:

• Mrs Nalini borrowed ₹ 26400 from a bank at the rate of 15% pcpa compounded annually.

To Find:

• Amount she has to pay at the end of 2 years and 4 months.

Formula Used:

When interest is compounded annually but time is a fraction:

$\sf{Suppose \;time\; is: a \dfrac{b}{c}. \;Then,}$

$\sf{Amount = Principal\bigg(1+\dfrac{Rate}{100}\bigg)^{a}\Bigg(1+\dfrac{\dfrac{b}{c}\times Rate}{100}\Bigg)}$

Where,

Principal = ₹ 26400

Rate = 15%

Time = 2 years 4 months

$\sf{=2\dfrac{4}{12}}\\\\=2\dfrac{1}{3}$

Substituting the values,

$\sf{Amount = 26400\bigg(1+\dfrac{15}{100}\bigg)^{2}\times\Bigg(1+\dfrac{\dfrac{1}{3}\times 15}{100}\Bigg)}$

$\sf{= 26400\bigg(1+\dfrac{15}{100}\bigg)^{2}\times\bigg(1+\dfrac{5}{100}\bigg)}$

$\sf{= 26400\bigg(\dfrac{100+15}{100}\bigg)^{2}\times\bigg(\dfrac{100+5}{100}\bigg)}$

$\sf{= 26400\bigg(\dfrac{115}{100}\bigg)^{2}\times\bigg(\dfrac{105}{100}\bigg)}$

$\sf{= 26400\bigg(\dfrac{23}{20}\bigg)^{2}\times\bigg(\dfrac{21}{20}\bigg)}$

$\sf{= 26400\times\dfrac{23}{20}\times\dfrac{23}{20}\times\dfrac{21}{20}}$

$\sf{= 264\!\!\!\not{0}\!\!\!\not{0}\times\dfrac{23}{2\!\!\!\not{0}}\times\dfrac{23}{2\!\!\!\not{0}}\times\dfrac{21}{20}}$

$\sf{=\dfrac{29,32,776}{80}}\\\\= 36,659.7$

Hence, Mrs. Nalini Shetty has to pay ₹ 36,659.7 at the end of 2 years and 4 months.