2.2
(part 1)
(1+r)n=2
ln(1+r)n=ln2
nln(1+r)=ln2
nr ≈ ln2
n ≈ ln2 / r
n ≈ ln2 / (i / 100)
n ≈ 0.69 / (i / 100)
∴ n ≈ 69 / i
(part 2)
条件 r ≈ 0.08.
(1+r)n=2
ln(1+r)n=ln2
nln(1+r)=ln2
n(r-(1/2)r2) ≈ ln2
n ≈ ln2 / (r - (1 / 2)r2)
n ≈ ln2 / r / (1 - (1 / 2)r)
n ≈ 0.69 / (i / 100) / (1 - (1 / 2)0.08)
∴ n ≈ 72 / i
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