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a)
$15,000 × (1+4.5%/12)^(4×12) - $15,000
= $17,952.22 - $15,000
= $2,952.22

bi)
$15,000 × (1+4.5%/2)^(3×2)
= $17,142.38

bii)
$17,142.38 - $15,000
= $2,142.38

ci)
Yr2 : 4%+0.5% = 4.5%
Yr3 : 4.5% + 0.5% = 5%
Yr4 : 5% + 0.5% = 5.5%

cii)
$15,000 × 1.04 × 1.045 × 1.05 × 1.055 - $15,000
= $3,058.54

d)
Plan A's interest : $2,952.22
Plan B's interest : $17,142.38 × (1+5%/2)^2 - $15,000
=$3,010.21
Plan C's interest : $3,058.54
Therefore, plan C is the best.

(a) 用plan A, 4年後可得利息:
$15,000 x (1+ 4.5%/12)^48 - $15,000
= $17,952.22 - $15,000
= $2,952.22

(b)(i) 用plan B, 3年後可得本利和:
$15,000 x (1 + 4.5%/2)^6
= $17,142.38

(b)(ii) 用plan B, 3年後可得利息:
$17,142.38 - $15,000
= $2,142.38

(c)(i) 用plan C, 第2, 3, 4年利息分別是:
2nd year = 4% + 0.5% = 4.5%
3rd year = 4.5% + 0.5% = 5.0%
4th year = 5.0% + 0.5% = 5.5%

(c)(ii)用plan C, 4年後可得利息:
$15,000 x (1+4%) x (1+4.5%) x (1+5.0%) x (1+5.5%) - $15,000
= $18,058.54 - $15,000
= $3,058.54

(d)
如用plan A, 4年後可得利息 $2,952.22

如用plan B, 4年後可得利息:
= $17,142.38 x (1+5%/2)^2 - $15,000
= $18,010.21 - $15,000
= 3,010.21

如用plan C, 4年後可得利息 $3,058.54

所以, 李先生應用plan C, 因用plan c在4年後可得最多利息。