A Home Purchased for $105,000 Increases by 3% of Its $a _ { n } = 105,000 ( 1.03 ) ^ { n } \text { for } n \geq 1$

Multiple Choice

A home purchased for $105,000 increases by 3% of its value each year. The value of the home after n years is given by $a _ { n } = 105,000 ( 1.03 ) ^ { n } \text { for } n \geq 1$ Find the value of the home after 5 years by computing $a _ { 5 }$ . Round to the nearest dollar.

A) $a _ { 5 } = \$ 121,724$
B) $a _ { 5 } = \$ 3,898,580$
C) $a _ { 5 } = \$ 389,858$
D) $a _ { 5 } = \$ 1,217,238$