金融関連の問題の計算方法を教えてください

質問

英語の質問です。

1. A zero coupon bond with a face value of $1,000 is trading at $960. It is maturing in 1 year. What is the yield on the bond?

2. Bond B is a 6% coupon bond with a par value of $1,000 that pays interests semi-annually with 3 years to maturity. The price of the bond is $1,054. What is the yield?

3. Bank A pays a nominal interest rate of 7.5%. If the interest is compounded monthly, what is the effective interest rate?

4. An instrument pays a compound interest rate of 6% per annum for 5 years. If you invest $10,000 now what will be the future value of the investment?

5. A $100 deposit pays 8% interest and is compounded monthly. One year later the deposit is worth?

6. The interest rate of a 1-year deposit in Australian dollar (AUD) is 6.0% p.a. and the interest rate of a 1-year deposit in Euro (EUR) is 3.5%. If the 1-year forward rate between AUD and EUR is quoted at AUD1.6468 per EUR, what is the spot rate of AUD per EUR?

計算方法を教えて頂けたら助かります。宜しくお願い致します。

回答No.1

xexstyle · ベストアンサー

1. A zero coupon bond with a face value of $1,000 is trading at $960. It is maturing in 1 year. What is the yield on the bond?

1,000/960-1 = 0.04167 = 4.167%

2. Bond B is a 6% coupon bond with a par value of $1,000 that pays interests semi-annually with 3 years to maturity. The price of the bond is $1,054. What is the yield?

利回りをrとすると次の式が成り立ちます。
-1054 = 1000×6%/2/(1+r/2) + 1000×6%/2/(1+r/2)^2 + 1000×6%/2/(1+r/2)^3 + 1000×6%/2/(1+r/2)^4 + 1000×6%/2/(1+r/2)^5 + 1000×(1+6%/2)/(1+r/2)^6
この式からrを求めると、4.07%となります。
この計算はExcelでも使わないと計算できません。
上の計算は複利での利回りの計算式です。
日本では単利での利回りもよく使われますが、外国では一般的ではありません。
なお、＾の記号はべき乗（るい乗）を表します。

3. Bank A pays a nominal interest rate of 7.5%. If the interest is compounded monthly, what is the effective interest rate?

(1+7.5%/12)^12 - 1 = 0.0776 = 7.76%

4. An instrument pays a compound interest rate of 6% per annum for 5 years. If you invest $10,000 now what will be the future value of the investment?

10,000×(1+6%)^5 = 13,382.26

5. A $100 deposit pays 8% interest and is compounded monthly. One year later the deposit is worth?

100×(1+8%/12)^12 = 108.30

6. The interest rate of a 1-year deposit in Australian dollar (AUD) is 6.0% p.a. and the interest rate of a 1-year deposit in Euro (EUR) is 3.5%. If the 1-year forward rate between AUD and EUR is quoted at AUD1.6468 per EUR, what is the spot rate of AUD per EUR?

現在の1AUDは、一年後には、1A×(1+6%) になる。
同じく現在の1EURは、一年後には、1EUR×(1+3.5%)になる。
この比率が、1.6468であるから、1.6468 = 1A×(1+6%) ÷1EUR×(1+3.5%)
これより、1A/1EUR = 1.6468×(1+3.5%)÷(1+6%) = 1.6080

お礼

早速分かりやすいご回答をありがとうございました。
手計算では難しいのですね。けれど計算方法の考え方がよく理解できました。
深謝致します。

補足

すみません。追加ですが、こちらはどう考えればいいのでしょうか。

Calculate the price of a treasury bill with face value of HKD200, yield of 5 percent per annum and 90 days until maturity. Assume 360 days in a year.

200÷(price of treasury bill) － 0.25 (90日なので) = 5%

という計算式で正しいのでしょうか？違う気がするのですが…。

宜しくお願い致します。