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A small business expects an income stream of $4000 per year for a four year peri

ID: 2833855 • Letter: A

Question

A small business expects an income stream of $4000 per year for a four year period.

(a) Find the present value of the business if the annual interest rate, compounded continuously, is the following.

Round your answers to two decimal places.

(i) 2%

Present Value = $ ______________________

(ii) 8%

Present Value = $_______________________

(b) In each case, find the value of the business at the end of the four-year period. Round your answers to two decimal places.

(i) Value =$__________________

(ii) Value=$___________________

Explanation / Answer

Compound Interest = P(1+r/100)n ,
where P : present value,
r : rate of interest
n : no. of years

Income is 4000$ per year, at the end of 4 years C.I. should be $16000
a)

(i) 16000 = P (1+2/100)4
P = $14781.53

(ii) 16000 =  P (1+8/100)4
P = $11760.48

b)

Value of company at the end of fourth year = Value of company in the starting of first year + interests applied for 4 years
(i) Value = $14781.53 + $16000 = $30781.53

(ii) Value = $11760.48 + $16000 = $27760.48