Question

An article valued at $P when new, depreciates by 10% of it's value at the end of every year. if at the end of the third year ,the article is valued at $7,290 . find the value of P.​

Answer 1

★Understanding The Question properly

• It is Given that the Principal when it start and the Rate is in Depreciate by 10% at the End of every Year . Now at the end of 3 year's the price of an article be $7,290.

From the Above Statement We get

• Rate of Depreciates = 10%
• Time = 3 year's
• Amount of article = $7,290

To Find

• Principal

Note: If the compounding frequency per annum is 1 i.e. if the interest is compounded annually, the compound interest formula is given as:

we know that

• If rate is in depreciates then Amount Formula will be

$\underline {\boxed{\bf{Amount= Principal \Bigg\{ 1-\dfrac{Rate \:}{100}\Bigg\}}^{time}}}$

• Putting the value of Amount, rate of Depreciate and time in formula we get

$\\\sf{~~~~~~:\implies 7290= Principal \Bigg\{ 1-\dfrac{10}{100}\Bigg\}^3}$

$\sf{~~~~~~:\implies 7290= Principal \Bigg\{ \dfrac{100 - 10}{100}\Bigg\}^3}$

$\sf{~~~~~~:\implies 7290= Principal \Bigg\{ \dfrac{90}{100}\Bigg\}^3}$

$\sf{~~~~~~:\implies 7290= Principal \times \dfrac{9 \times 9 \times 9 }{10 \times 10 \times 10}}$

$\sf{~~~~~~:\implies Principal = \dfrac{ 7290\times 1000}{729}}$

$\sf{~~~~~~ :\implies Principal = \dfrac{ \cancel{729}^{1} \: 0\times 1000}{ \cancel{729}}}$

$\sf{~~~~~~ :\implies Principal = 10000}$

• $\pink{\text{The Value of Principal is \bf{\ 10,000.}}}$

Answer 2

Answer:

10,000

Step-by-step explanation:

this is your correct answer