Question

calculate the amount of 31250 rupees at the end of 5/2 years. compounded annually at 8% per annum​

Answer 1

Answer:

• The amount is ₹ 37908.

Step-by-step explanation:

Given that:

$\sf\circ\;\;Principal = Rs.\;31250$

$\sf \circ\;\;Rate = 8\% \;per\; annum$

$\sf{\circ \;\;Time = \dfrac{5}{2}\;years=2\dfrac{1}{2}\;years}$

As we know that:

When we have time in fraction

$\sf{i.e. \longrightarrow\;a\dfrac{b}{c}\;years.\;\bf{Then,}}$

$\sf{Amount=P\bigg(1+\dfrac{R}{100}\bigg)^a+\left(1+\dfrac{\dfrac{b}{c}\times R}{100}\right)}$

As,

$\sf{Time\;is\;2\dfrac{1}{2}\;years}$

Therefore,

Substituting the values,

$\sf{Amount=31250\bigg(1+\dfrac{8}{100}\bigg)^2+\left(1+\dfrac{\dfrac{1}{2}\times 8}{100}\right)}$

Solving the brackets,

$\sf{\longmapsto31250\left(\dfrac{100+8}{100}\right)^2\times\left(1+\dfrac{4}{100}\right)}$

$\sf{\longmapsto31250\left(\dfrac{108}{100}\right)^2\times\left(\dfrac{100+4}{100}\right)}$

$\sf{\longmapsto31250\left(\dfrac{108}{100}\right)^2\times\left(\dfrac{104}{100}\right)}$

Opening the brackets,

$\sf{\longmapsto31250\times\dfrac{108}{100}\times\dfrac{108}{100}\times\dfrac{104}{100}}$

Reducing the numbers,

$\sf{\longmapsto31250\times\dfrac{27}{25}\times\dfrac{27}{25}\times\dfrac{26}{25}}$

Dividing the numbers,

$\sf{\longmapsto31250\times1.08\times1.08\times1.04}$

Multiplying the numbers,

$\sf{\longmapsto37908}$

Hence, amount is ₹ 37908.