Question

Company D showed a profit of $1.5 million last year. The CEO of the company expects the profit to increase by 0.04 million dollars each year over the next 5 years and the profits will be continuously invested in an account bearing a 4.5% APR compounded continuously.

(a) Write the flow rate, R, of the income stream. (Let t represent the number of years after the company showed a profit of $1.5 million.)
R(t) =  

0.04t+1.5

   million dollars per year

(b) Calculate the 5-year future value. (Round your answer to three decimal places.)
$  million

(c) Calculate the 5-year present value. (Round your answer to three decimal places.)
$  million

Answer 1

part a)

Flow rate is given as,

R(t)= 0.04t+1.5

part b) Future value =

Using integration by parts we get

Future value = 8.950 million

Part c)

Present value = 7.147 million

here is the work