Company C showed a profit of $1.1 million last year. The CEO of the company expe

Question

Company C showed a profit of $1.1 million last year. The CEO of the company expects the profit to decrease by 5% each year over the next five years and the profits will be continuously invested in an account bearing a 4.75% APR compounded continuously. Please, answers the three questions below: a. Write the flow rate, R, of the income stream. (Let t represent the number of years after the company showed a profit of $1.1 million.) R(t) =________________________Dollars per year b. Calculate the 5-year future value. (Round your answer to three decimal places.) $________________Milllion c. Calculate the 5-year present value. (Round your answer to three decimal places.) $_______________Million

Explanation / Answer

Profits are 1.1 , 1.045, 0.99275, 0.9431125

Profit = 1.1 * (0.95)^(t-1) for t>=1

Compound Interest Formula:

A=P(1+r)^t

where:

P=principal amount (the initial amount you borrow or deposit)

r =annual rate of interest (as a decimal)

t =number of years the amount is deposited or borrowed for.

A=amount of money accumulated after n years, including interest.

n= number of times the interest is compounded per year

So, R(t)= P1(1+r)^t + P2(1+r)^(t-1)+P3(1+r)^(t-2)+P4(1+r)^(t-3)+P5(1+r)^(t-4)

= 1.1*(1+r)^t+1.1 * (0.95)^1 *(1+r)^(t-1)+1.1*(0.95)^2 *(1+r)^(t-2)+ 1.1*(0.95)^3 *(1+r)^(t-3)+ 1.1*(0.95)^4 *(1+r)^(t-4)

where r=0.0475

(b) FV= $ 5.760 million

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