Question

Question 4 0/ 1 pts "Your machine operator is becoming more productive and generates additional proft each year. You expect to receive $27,000 in profit at the end of the year, but this will increase by 4% a year for the next 12 years. If you have a 16% annual interest rate on your investments (compounded annually), what is the Future Value of the profnts at the end of 12 years from now?" 164314

Answer 1

Profit in year 1 (A₁) = $27,000

Constant rate of increase in profit (g) = 4%

Annual interest rate (i) = 16%

Time period (n) = 12 years

STEP 1

Calculate the Present Value -

$Pg = A_{1}\left [ \frac{1-\left ( \frac{1+g}{1+i} \right )^{n}}{i-g} \right ]$

$Pg = 27000\left [ \frac{1-\left ( \frac{1+0.04}{1+0.16} \right )^{12}}{0.16-0.04} \right ]$

$Pg = 27000\left [ \frac{1-\left ( \frac{1.04}{1.16} \right )^{12}}{0.12} \right ]$

$Pg = 27000\left [ \frac{1-0.2697}{0.12} \right ]$

$Pg = 27000\left [ \frac{0.7307}{0.12} \right ]$

Pg = 164,316.6

STEP 2

Calculate the Future Value -

FV = Pg(F/P, i, n)

FV = 164,316.6 (F/P, 12%, 12)

FV = 164,316.6 * 3.8960

FV = 640,177.47

So,

The Future Value of the profits is $640,177.47