Fight Finance

Question 906  effective rate, return types, net discrete return, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its effective annual return be? Note that an effective annual return is also called a net discrete return per annum. If the price now is $P_0$ and the price in one year is $P_1$ then the effective annul return over the next year is:

$$r_\text{effective annual} = \dfrac{P_1 - P_0}{P_0} = \text{NDR}_\text{annual}$$

(a) 0%

(b) 30.102999566%

(c) 69.314718056%

(d) 100%

(e) 200%

Question 907  continuously compounding rate, return types, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its continuously compounded return $(r_{CC})$ be? If the price now is $P_0$ and the price in one year is $P_1$ then the continuously compounded return over the next year is:

$$r_\text{CC annual} = \ln{\left[ \dfrac{P_1}{P_0} \right]} = \text{LGDR}_\text{annual}$$

(a) 0%

(b) 30.102999566%

(c) 69.314718056%

(d) 100%

(e) 200%

Question 908  effective rate, return types, gross discrete return, return distribution, price gains and returns over time

For an asset's price to double from say $1 to $2 in one year, what must its gross discrete return (GDR) be? If the price now is $P_0$ and the price in one year is $P_1$ then the gross discrete return over the next year is:

$$\text{GDR}_\text{annual} = \dfrac{P_1}{P_0}$$

(a) 0%

(b) 30.102999566%

(c) 69.314718056%

(d) 100%

(e) 200%

Question 914  bill pricing, money market, return types

A bank bill was bought for $99,000 and sold for $100,000 thirty (30) days later. There are 365 days in the year. Which of the following formulas gives the simple interest rate per annum over those 30 days?

(a) $12.28956229\% = \left( \dfrac{100,000}{99,000} - 1 \right) \times (365/30)$

(b) $13.00694446\% = \left( \dfrac{100,000}{99,000} \right)^{365/30} -1$

(c) $12.60944895\% = \left( \left( \dfrac{100,000}{99,000} \right)^{(365/2)/30} -1 \right) \times 2$

(d) $12.2904215\% = \left( \left( \dfrac{100,000}{99,000} \right)^{(365/12)/30} -1 \right) \times 12$

(e) $12.22790862\% = \ln \left( \dfrac{100,000}{99,000} \right) \times 365/30$

Note: To help you identify which is the correct answer without doing any calculations yourself, the formulas used to calculate the numbers are given.