Find the value A of a principal P = $3000 set out at an interest rate r = 8 percent for time t = 6 years when compounded

(a) annually,

(b) semiannually,

(c) quarterly, and

(d) continuously.

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(a) From (11.7), A = 3000(1+.08)6 A = 3000(1.5868743) = $4760.62 .08 2(6) (b) From (118), with m = 2, A 3000 1+ 2 A = 3000(1+.04) 12 A = 3000(1.6010322) = $4803.10 .08 4(6) (c) From (118), with m = 4, (d) From (119), A 3000 1+ 4 A = 3000(1+.02)24 A 3000(1.6084373) = $4825.31 = A = 3000e (0.08)6 = 3000 0.48 A = 3000(1.6160744) = $4848.22