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A house is purchased for $145,000 and each year increases in value by 6% of its value the previous year. (6 marks) Let be the value of the house in year . Write a difference equation which gives the value of the house after years. Solve the difference equation. Find the projected value of the house in 15 years.

Sagot :

varshamittal029

The projected value of the house after 15 years is $347500.

A house is purchased for $145,000.

The value of the house increases each year by 6% of its value the previous year.

Let y(n) denote the value of the house after n years.

Initial value is $145,000.

⇒ y(0) = 145,000

The value of the house increases each year by 6% of its value the previous year.

Therefore the growth is exponential, and we have

y(n) = y(0)(1+0.06)ⁿ

When n = 1

⇒y(1) = 145000 × (1.06)

⇒y(1) = 153700

When n = 2,

⇒y(2) = 145000 × (1.06)²

⇒y(2) = 162922

Therefore, when n = 15,

⇒y(15) = 145000 × (1.06)¹⁵

⇒y(15) = 3,47,500

Therefore, the projected value of the house after 15 years is $347500.

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