Yahoo 知識+ 將於 2021 年 5 月 4 日 (美國東岸時間) 停止服務。從 2021 年 4 月 20 日 (美國東岸時間) 起，Yahoo 知識+ 網站將轉為僅限瀏覽模式。其他 Yahoo 資產或服務，或你的 Yahoo 帳戶將不會有任何變更。你可以在此服務中心網頁進一步了解 Yahoo 知識+ 停止服務的事宜，以及了解如何下載你的資料。

# Equity investment

1.Emma(of age 20 now) targets to save \$400,000 for marriage with her boyfriend, Joe, in the future. Both Emma and Joe are willing to contribute \$2,000 each per month( \$4,000 per month in total) for saving. Assume they invest in an equity with average return of 8.4% per year.Their first contribution will be made at the end

of each month

A. What is the periodic rate of this investment?

B.How long (in terms of years) will Emma and Joe have to save \$400,000 for

their marriage?Make any assumption(s) if you think necessary.Round up your

2.Peter is a stock trader and he is trading on a common stock ABC.

A. Peter purchased 5,000 shares of common stock ABC on margin at \$40 per share. Initial margin was 55%. How much did you borrow from the broker?

B.If the maintenance margin is 35%,below what stock price level would Peter get a Margin call? Assume the stock pays no dividend and ignore any interest on margin.

C.One week later, he closed the position by selling the ABC stock at shares price of \$50 per share. Assume that ABC common stock paid no dividend and the

interest on margin was 5% per annum. What is the rate of return for Peter’s investment, if Interest on margin is taken into consideration? (assume there are 52 weeks per year)

### 3 個解答

• 6 年前
最愛解答

請問回答後你會否刪帖？？

2015-06-14 18:01:49 補充：

讓我先講解一下 annuity (年金) 的現值 (present value) 和 期值/終值/將來值 (future value) 的公式。

假設

✿ 投資期限是 n 個時期

✿ 每時期的 effective interest 是 i (per period)

✿ 付款方式是「時期尾」時付，即 annuity-immediate

那麼，年金的現金流如下：

＄１　＄１　　　　＄１

｜　　｜　．．．　｜

Ｖ　　Ｖ　　　　　Ｖ

＋－－＋－－＋－－－－－＋－＞　時間

０　　１　　２　．．．　ｎ

2015-06-14 18:04:16 補充：

PV = 現值 = 這批 \$1 於 時間０ 時的價值

FV = 終值 = 這批 \$1 於 時間ｎ 時的價值

PV

= 1/(1 + i) + 1/(1 + i)² + ... + 1/(1 + i)ⁿ

= 1/(1 + i)[1 - 1/(1 + i)ⁿ] / [1 - 1/(1 + i)]

= [1 - 1/(1 + i)ⁿ] / i

2015-06-14 18:04:50 補充：

FV

= (1 + i)ⁿ⁻¹ + (1 + i)ⁿ⁻² + ... + (1 + i) + 1

= 1 + (1 + i) + ... + (1 + i)ⁿ⁻² + (1 + i)ⁿ⁻¹

= [(1 + i)ⁿ - 1] / [(1 + i) - 1]

= [(1 + i)ⁿ - 1] / i

明白這兩條公式嗎？

2015-06-14 18:39:07 補充：

Question 1.

簡單一點綜合題意，每月儲 \$4000，月尾供款，年利率 8.4%，問何時才能儲得 \$400000。

(a)

Periodic rate of return

= Effective monthly rate

= Nominal annual rate / 12

= 8.4% / 12

= 0.7%

(b)

Let x be the required number of years.

The investment period is then n = 12x months.

FV = 400000

4000 × (1.007ⁿ - 1)/0.007 = 400000

1.007ⁿ = 1.7

ln(1.007ⁿ) = ln(1.7)

n ln(1.007) = ln(1.7)

n = ln(1.7)/ln(1.007)

n = 76.06904154

x = n/12 = 6.339084795

They need 6.34 years to save \$400000.

Assumption: The interest rate remains constant.

✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀ ✿ ❀

Question 2.

(a)

Amount borrowed

= Liability (L)

= \$40 × 5000 × (1 - 55%)

= \$90000

(b)

Stock purchased

= Asset (A)

= \$40 × 5000

= \$200000

Own contribution

= Equity (E)

= \$40 × 5000 × 55%

= \$110000

Margin = E/A = (A - L)/A

Note that L is not changed with stock price.

Let \$P be the required price level to get a margin call.

(5000P - 90000)/5000P = 35%

5000P(1 - 35%) = 90000

P = 90000/[5000(0.65)]

P = 27.69230769

The required price level is \$27.69.

(c)

Rate of return

= (Gain on the stock investment - Interest on margin)/(Own contribution)

= [5000 × (50 - 40) - 90000 × 5%/12 ] / 110000

= 49625/110000

= 0.451136364

≈ 45.11%

• 6 年前

為什麼會這樣問?THX

2015-06-14 18:13:00 補充：

我明這兩條公式,但我係唔明D 文字,所以唔識

• 6 年前

本來我都想答,多謝提醒.