Solution:
we are given that
Sharon is 18 and would like to buy a house when she is 34.
it mean [tex] n=34-18=16 [/tex]
we have been asked to find the discount factor for today's prices if the housing values increase 7% per year?
It mean [tex] r=0.07, Annual \ Compounding. [/tex]
As we know that
[tex] A=p(1+r)^{nt} [/tex]
Let current price be 100, then the future price will be
[tex] A=100(1+0.07)^{16*1}=100(1.07)^{16}\\
\\
A=100*2.952=295.2\\
\\
[/tex]
Hence the discount factor is [tex] =\frac{100}{295.2} *100=33.87 Percent [/tex]
Hence the correct option is 33.9%.
