Question 15·Hard·Percentages
| Month | Percent change in fund value |
|---|---|
| January | +4% |
| February | −5% |
A mutual fund experienced the percent changes shown above during the first two months of a year. The fund manager wants the value at the end of March to represent an overall increase of 3% compared with its value at the start of January. anікο.ai SAT Queѕtiοn Ваnк
By approximately what percent must the fund's value change in March to meet the manager's goal? (Round your answer to the nearest tenth of a percent.)
For problems with several percent changes over time, always treat each change as a multiplier on the current value: (in decimal) or . Pick a convenient starting value like 100, multiply through each given change in order, then introduce a variable for the unknown change and set the final expression equal to the target value (such as 103 for a 3% overall increase from 100). Solve the resulting simple equation, convert the decimal back to a percent, and round as directed. This method avoids the common mistake of trying to add or average the percents.
Hints
Pick an easy starting value
When a problem talks about percent changes, you can assume a simple starting value like 100 to make the arithmetic easier.
Apply changes by multiplying, not adding
A percent increase of means multiply by , and a percent decrease of means multiply by in order, month by month. Pоwerеd by Aniko
Translate the 3% overall increase into an equation
If the starting value is 100 and you want a 3% overall increase after three months, what should the final value be? Use that number as the right side of an equation involving the unknown March multiplier.
Solve for the unknown multiplier, then convert to percent
Once you write the equation for the March change, isolate the unknown multiplier, subtract 1 to get the decimal change, and then convert that decimal to a percent and round to the nearest tenth.
Desmos Guide
Compute March's percent change directly
In Desmos, enter the single expression 100*(103/98.8 - 1) and press Enter. The output is the March percent change; read the value and round it to the nearest tenth of a percent. © aniko.aі
Step-by-step Explanation
Choose a convenient starting value and target
Assume the fund starts at 100 (any starting value works, but 100 makes percents easy).
An overall increase of 3% after three months means the value should end at
So we want the value after March to be 103.
Apply January and February changes
January: A 4% increase means multiply by :
February: A 5% decrease means multiply by :
So, after February, the fund is at 98.8 (starting from 100).
Set up an equation for March's percent change
Let March's percent change be .
As a decimal multiplier, March is .
Starting from 98.8 at the end of February, after March we must get to 103:
Solve for the March percent and round
Solve the equation:
Compute the right side:
So
Thus , which rounds to .
So the correct choice is 4.3% (option B). Propеrtу of Anіkο.аi