Answer: Option B : Accessible
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The applicable formula is;
A = P(1-r)^n
Where;
A = Final purchasing power
P = Current purchasing power
r = inflation
n = Number of years when P changes to A
Confirming the first claim:
A = 1/2P (to be confirmed)
P = $3
r = 7% = 0.07
n = 10.25 years
Using the formula;
A = 3(1-0.07)^10.25 = 3(0.475) ≈ 3(0.5) = $1.5
And therefore, A = 1/2P after 10.25 years.
Now, give;
P = $9
A = 1/4P = $9/4 = $2.25
r = 6.5% = 0.065
n = ? (nearest year).
Substituting;
2.25 = 9(1-0.065)^n
2.25/9 = (1-0.065)^n
0.25 = (1-0.065)^n
ln (0.25)= n ln(1-0.065)
-1.3863 = -0.0672n
n = (-1.3863)/(-0.0672) = 20.63 years
To nearest year;
n = 21 years
Therefore, it would take approximately 21 years fro purchasing power to reduce by 4. That is, from $9 to $2.25.
The mean of salary for these options is $30.76
