Asked by Kelsey Michalak on Jun 14, 2024
Verified
How much will an investment of $100 be worth after 20 years if it increases in value by 25% in half of the years, but declines by 20% in the other years?
Increases In Value
A financial term indicating an asset's worth grows over time due to various factors like market demand.
Declines
Decreases in value, performance, or level over a period of time.
- Evaluate the effect of compounding intervals on the growth or reduction of an investment.
- Conduct break-even evaluations on investments following gains and losses.
Verified Answer
TC
Tyler CarlomustoJun 20, 2024
Final Answer :
For a 25% increase, 1 + c = 1.25. For a 20% decrease, 1 + c = 0.8. Note that 1.25 x 0.8 = 1.00. That is, a 20% decrease exactly offsets a 25% increase. Since we have the same number of 25% increases as 20% decreases, the investment's value will be unchanged (at $100) after 20 years.
Learning Objectives
- Evaluate the effect of compounding intervals on the growth or reduction of an investment.
- Conduct break-even evaluations on investments following gains and losses.