1. Suppose an investment is expected to generate income at the rate of R ( t ) =
ID: 2854060 • Letter: 1
Question
1. Suppose an investment is expected to generate income at the rate of
R(t) = 200,000
dollars/year for the next 6 years. Find the present value of this investment if the prevailing interest rate is 8%/year compounded continuously. (Round your answer to the nearest whole number.)
2. Camille purchased a 12-year franchise for a computer outlet store that is expected to generate income at the rate of
R(t) = 400,000
dollars/year. If the prevailing interest rate is 10%/year compounded continuously, find the present value of the franchise. (Round your answer to the nearest whole number.)
$
Explanation / Answer
1) P = [0 to 6] R(t) e-rt dt
Here P = present value , r = interest rate = 8% = 0.08
t = time
==> P = [0 to 6] (200000) e-0.08t dt
==> P = [0 to 6](200000)e-0.08t/(-0.08)
==> P = (-200000/0.08)(e-0.08(6) - e-0.08(0))
==> P = 953041.5205
==> P = $953042
Hence present value = $953042
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