Final answer:
This high school level question asks how to compute the year when the target balance of an investment is reached using the compound interest formula. A while loop is utilized to iteratively compound the interest and to determine when the target balance is reached, displaying the balance each year and rounding to two decimal places.
Step-by-step explanation:
The question involves the mathematical concept of compound interest, which is a core topic in financial mathematics. To help a student compute the year when an investment balance reaches the target balance, they need to understand how the interest on an investment compounds over time. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested or borrowed for
To calculate the year in which the target balance is reached, you would use a while loop in programming or sequential calculation in mathematics, to iterate through each year, compounding the interest and checking if the current balance has reached or exceeded the target balance. With each iteration, the investment value is updated using the compound interest formula, and the balance is rounded to two decimal places. By repeatedly multiplying the investment by (1 + annual interest rate), you calculate the new balance for each subsequent year.
Example:
- Prompt the user for the initial investment amount, annual interest, and target balance.
- Initialize a variable to keep track of the current year.
- Use a while loop to calculate the compound interest for each year.
- Check if the current balance has reached the target balance.
- If the target balance is reached, display the year and break out of the loop; otherwise, continue to the next iteration