Using proportions, it is found that:
- a) The annual rate of increase in the value of the house was of 15.24%.
- b) In 1950, the house was valued at $4,029.
Item a:
From an initial value of $60,000, the house increased in value by $375,000, as 435000 - 60000 = 375000.
The percent increase is given by:
[tex]\frac{375000}{60000} \times 100\% = 625\%[/tex]
In 2003 - 1962 = 41 years, hence:
[tex]r = \frac{625}{41} = 15.24[/tex]
The annual rate of increase in the value of the house was of 15.24%.
Item b:
The value increases 15.24% a year, hence, in t years after 1962, considering an initial value of $60,000, the value is:
[tex]V(t) = 60000(1.1524)^t[/tex]
1950 is 12 years before 1950, hence the value is V(-12), that is:
[tex]V(-12) = 60000(1.1524)^{-12} = \frac{60000}{(1.1524)^{12}} = 4029[/tex]
In 1950, the house was valued at $4,029.
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