**Question 542** price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to **double** every **10** years, what must be the expected future capital return, given as an effective annual rate?

**Question 543** price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to **triple** every **5** years, what must be the expected future capital return, given as an effective annual rate?

**Question 579** price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to **double** if the price grows by **10**% pa?

**Question 580** price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to **quadruple** (be four times as big, say from $1 to $4) if the price grows by **15**% pa?

**Question 742** price gains and returns over time, no explanation

For an asset's price to quintuple (be five times as big, say from $1 to $5) every **5** years, what must be its effective annual capital return?

**Question 743** price gains and returns over time, no explanation

How many years will it take for an asset's price to **triple** (increase from say $1 to $3) if it grows by **5**% pa?

**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}###**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}###**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}###**Question 915** price gains and returns over time, IRR, NPV, income and capital returns, effective return

For a share price to **double** over **7** years, what must its capital return be as an effective annual rate?

**Question 1085** inflation, consumer price index, price gains and returns over time, arithmetic and geometric averages

Calculate the annual inflation rate between 30th September 1948 when the consumer price index (CPI) was **3.7** and 31st December 2023 when the CPI was **136.1**, as published by the ABS. Note that you should find the annual CPI inflation rate between these dates.

The annual inflation rate over these **75.25** (=2024 - 1948.75) years was: