(A) The initial cost of the machine is $P = 15625$.The rate of depreciation is $r = 20\% = 0.2$.The value of the machine after $n = 5$ years is given

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(A) The initial cost of the machine is $P = 15625$.The rate of depreciation is $r = 20\% = 0.2$.The value of the machine after $n = 5$ years is given by the formula $V = P(1 - r)^n$.$V = 15625 \times (1 - 0.2)^5$$V = 15625 \times (0.8)^5$$V = 15625 \times \left(\frac{4}{5}\right)^5$$V = 15625 \times \frac{1024}{3125}$$V = 5 \times 1024 = 5120$Thus,the estimated value at the end of $5$ years is $Rs. 5120$.

Class 11 Mathematics Sequences and Series Geometric progression

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$A$ manufacturer reckons that the value of a machine,which costs him $Rs. 15625$,will depreciate each year by $20\%$. Find the estimated value at the end of $5$ years.

A
$Rs. 5120$
B
$Rs. 6250$
C
$Rs. 4096$
D
$Rs. 8192$

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Sequences and Series

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Geometric progression

If $r > 1$,$x = a + \frac{a}{r} + \frac{a}{r^2} + \dots \infty$,$y = b - \frac{b}{r} + \frac{b}{r^2} - \dots \infty$,and $z = c + \frac{c}{r^2} + \frac{c}{r^4} + \dots \infty$,then $\frac{xy}{z} = \dots$

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If the $10^{th}$ term of a geometric progression is $9$ and the $4^{th}$ term is $4$,then its $7^{th}$ term is:

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Let $n (> 1)$ be a positive integer. The largest integer $m$ such that $(n^m + 1)$ divides $(1 + n + n^2 + \dots + n^{127})$ is:

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$A$ manufacturer reckons that the value of a machine,which costs him $Rs. 15625$,will depreciate each year by $20\%$. Find the estimated value at the end of $5$ years.

Similar Questions

If $r > 1$,$x = a + \frac{a}{r} + \frac{a}{r^2} + \dots \infty$,$y = b - \frac{b}{r} + \frac{b}{r^2} - \dots \infty$,and $z = c + \frac{c}{r^2} + \frac{c}{r^4} + \dots \infty$,then $\frac{xy}{z} = \dots$

If the $5^{th}$ term of a $G.P.$ is $\frac{1}{3}$ and the $9^{th}$ term is $\frac{16}{243}$,then the $4^{th}$ term will be:

If the $10^{th}$ term of a geometric progression is $9$ and the $4^{th}$ term is $4$,then its $7^{th}$ term is:

What is the geometric mean of $3, 3^2, 3^3, \dots, 3^n$?

Let $n (> 1)$ be a positive integer. The largest integer $m$ such that $(n^m + 1)$ divides $(1 + n + n^2 + \dots + n^{127})$ is:

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