The present value (PV) of an investment that provides income continuously at a rate R(t) $/year for T years, and earns interest at rate r, isWe think of present value as the payment that we would need to receive at t = 0 so that at time T the payment’s value would be the same as the amount accumulated from the income stream (with both accumulating interest). Find the PV if R(t) = 5000 + 100t $/year, r = 0.05, and T = 10 years.

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T R(t)e-t dt.