SOLUTION: If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . Accordi

Question 107480: If a piece of real estate purchased for $50,000 in 1998 appreciates at
the rate of 5% per year, then its value t years after the purchase will
be f (t) = 50,000(1.05t ) . According to this model, by how much will the
value of this piece of property increase between the years 2007 and
2008?
a. $2500
b. $3140
c. $3880
d. $31,400
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
First, a correction.
If the property appreciates 5% every year, then after the first year,1999.
F(1)=50000(1.05)
After the second year, 2000.
F(2)=F(1)*(1.05)=50000(1.05)(1.05)=
The equation should be

then
2007 would be the 9th year and 2008 would be the 10th year.
and

or
and

The difference between the 10th year and the 9th year would then be

C.3880, close enough.
If you used the original equation, the house value increases only $2500,
after the first year but then increases value by $52,500 every year after.
At the end of the 10th year, the house would be worth $525,000.
That would be a great profit.
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