If a student successfully completes an MBA program in 2 years, he will earn $50,000 more than what he could earn without the degree for his lifetime. Calculate the present value of this perpetual rise in his income associated with the degree. The rate of interest in the market is 10%.
My attempt:
He will earn \$50,000 more at the end of his 1st year at the job. Let the present value of this increase be $PV_1$.
$\displaystyle 50,000=PV_1\left(1+\frac{10}{100}\right)^3$
The exponent is 3 because he will spend the next 2 years attending the MBA program and be paid at the end of the 3rd year.
$\implies 50,000=PV_1\times(1.1)^3$
$\displaystyle PV_1=\frac{50,0000}{(1.1)^3}$
$\displaystyle PV_2=\frac{50,000}{(1.1)^4}$
and so on.
$\begin{aligned}[t] PV&=PV_1+PV_2+\ldots \\ &=\frac{50,000}{(1.1)^3}+\frac{50,000}{(1.1)^4}+\ldots \\ &=\frac{50,000}{(1.1)^3}\times\frac{1}{1-\frac{1}{1.1}} \\ &=\frac{50,000}{(1.1)^3}\times\frac{1.1}{0.1} \\ &=\frac{500,000}{(1.1)^2} \\ \end{aligned}$
The answer given by the professor is "PV of lifetime increase in salary is $500,000." Where have I gone wrong?
