Question

Roger’s home originally cost him $165,000. For the first six years he lived there, his house grew in value at a rate of 1.6% per year. After that, his property value increased by 3.9% per year for the next eight years. To the nearest hundred dollars, how much had Roger’s home increased in value after fourteen years?
a.
$76,200
b.
$75,600
c.
$81,500
d.
$56,400

Answer 1

Value after 14 years = 165000*(1.016)^6*(1.039)^8.

Compute:
(1.016)^6 ≈ 1.0999229
(1.039)^8 ≈ 1.35807696
Product ≈ 1.49378013

Final value ≈ 165000 * 1.49378013 ≈ 246,476.72

Increase ≈ 246,476.72 − 165,000 = 81,476.72 → to the nearest hundred: $81,500.

Answer: c. $81,500