The capital value (present sale value) CV of property that can be rented on a pe

Question

The capital value (present sale value) CV of property that can be rented on a perpetual basis for R dollars annually is given by CV = integral_0^infinity Re^-it dt where i is the prevailing continuous interest rate. Show that CV = R/i. CV ~ integral_0^infinity Re^-it dt = lim_b rightarrow infinity integral_0^d Re0-it dt = lim_b rightarrow infinity Find the capital value of property that can be rented at $10#000 annually when the prevailing continuous interest rate is 6%/year. (Round your answer to the nearest whole number.)

Explanation / Answer

Solution of part (a)

CV= lim b->infinite [integral from 0 to b (Re^-it).dt]

Integrating (Re^-it) from 0 to b with respect to 't' will yield result as below-

=> lim b->infinite [R/(-i)](e^-ib - 1)

Now apply limit of b-> infinity

=> R/(-i) * (0-1) = R/i (Hence proved)

Solution of part (b)

Given that R=10000$ , i= 0.06

CV= 10000/(0.06) = 166666.67

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