Question

Mr and mrs boyce bought a house for 96000 in 1995. the real estate broker indicated that houses in their area were appreciating at an average annual rate at 7%. if the appreciation remained steady at this rate, what was the value of the boyce's home in 2009?

Answer 1

A house is valued every year. The building is appreciating at an average annual rate of 7%. Therefore, every year the value of the house is increasing.

                 Start Year                       End Year 
1995       96,000.00   1.07               102,720.00
1996     102,720.00   1.07               109,910.40
1997     109,910.40   1.07               117,604.13
1998     117,604.13   1.07               125,836.42
1999     125,836.42   1.07               134,644.97
2000     134,644.97   1.07               144,070.11
2001     144,070.11   1.07               154,155.02
2002     154,155.02   1.07               164,945.87
2003     164,945.87   1.07               176,492.08
2004     176,492.08   1.07               188,846.53
2005     188,846.53   1.07               202,065.79
2006     202,065.79   1.07               216,210.39
2007     216,210.39   1.07               231,345.12
2008     231,345.12   1.07               247,539.28
2009     247,539.28   1.07               264,867.03

Boyce's home is valued at $264,867.03 at the end of 2009.

Or it can be valued using the Future Value formula:

FV = (1+r)^n * PV

PV = 96,000
r = 7%
n = 15 years

FV = (1 + 0.07)¹⁵  x 96,000
FV = (1.07)¹⁵ x 96,000
FV = 2.759 x 96,000
FV = 264,864