Find the present value of $1000 to be paid 4 years from now when the current interest rate is 6 percent if interest is compounded

(a) annually,

(b) quarterly, and

(c) continuously.

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(a) From (1116), Substituting, P = A(1+r) P = 1000(1+.06)-4 Entering 1.06 on a calculator, hitting the key, then entering 4 followed by the key to make it negative, and finally activating the = key, as explained in Section 1.7.11, P = 1000(0.79209) = $792.09 (b) From (11.17), P = A (1 + 2) -mt - m -4(4) .06 Substituting, = P 1000 1+ = 1000(1+.015)-16 4 (c) From (11.18), Substituting, P = 1000(0.78803) = $788.03 P = Aert P: = 1000e (0.06)(4) = 1000e0.24 P=1000(0.78663) = $786.63