Basic equivalence

2015.1.21
FE演習（第14週）
－Economic Optimization －
Basic equivalence
2. How much must be invested on January 1, year 1, in order to
accumulate $2,000 on January 1, year 6 at 6%?
1回預けるのみの場合
投資（原価）額＝ F(終価) × （1＋利率）－年数
投資額 = $2,000×1.06-5 = $1495
Basic equivalence
6. How much must be deposited at 6% each year beginning on
January 1, year 1, in order to accumulate $5000 on the date of the
last deposit, January 1, year 6?
定期的に預ける場合
積立額＝ F(終価) ×
0.06
投資額 = $5,000×
(1 + 0.06)6 – 1
利率
（1＋利率）年数－1
= $717
Basic equivalence
8. If $500 is invested now, $700 two years from now, and $900
four years from now (all at 4%), what will be the total amount in
ten years?
1回預けるのみの場合
F(終価) ＝投資（原価）額 × （1＋利率）年数
F= $500×1.0410 + $700×1.048 + $900×1.046 = $2837
Economic Optimization
13
0.05
積立額 = $20,000× (1 + 0.05)19 – 1 = $654
Annual cost
21. A small building can be reroofed for $6000 (aluminum) or
$3500 (shingles). The estimated lives are 50 years and 15years,
respectively. If the interest rate is 10%, which alternative is
superior?
A(年価) ＝投資（原価）額 ×
アルミニウムの平均年間費用
＝購入コスト×資本回収係数＝$6,000×
＝$605
こけら板の平均年間費用
＝購入コスト×資本回収係数＝$3,500×
＝$460
こけら板の方が勝っている。
利率×（1＋利率）年数
(1＋利率)年数－1
0.10×(1 + 0.10)50
(1＋0.10)50－1
0.10×(1 + 0.10)15
(1＋0.10)15－1
Rate of Return
24. A speculator in land and property pays $14,000 for a house that
he expects to hold for ten years. $1,000 is spent in renovation and
a monthly rent of $75 is collected from the tenants who live in
house. (Assume all rent is paid at the end of the year.) Taxes are
$150 per year and maintenance costs are $250 per year. What must
the sales price be in ten years to realize a 10% rate of return?
n年後の売却価格
＝（購入コスト＋改修費用）×終価係数
＋（税金＋メンテナンスコスト）×年金終価係数－年間家賃×年金終価係数
10年後の売却コスト
＝（$14,000＋$1,000）×（1＋0.10）10
＋（$150×$200)×
＝$30,937
(1 + 0.10)10－1 －（$75×12）× (1 + 0.10)10－1
0.10
0.10

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