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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