Final answer:
To calculate the return needed to bring investments from $9,800 to $11,000 in two years, use the compound interest formula rearranged to solve for the annual rate (r) as (A/P)^(1/n) - 1, plugging in A as $11,000, P as $9,800, and n as 2.
Step-by-step explanation:
To compute the return needed to increase an investment from its current value of $9,800 to a target value of $11,000 in the next two years, one can use the formula for compound interest. The formula is:
A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and n is the number of years the money is invested.
However, solving for r (the rate) when you know the final amount (A), the principal (P), and the number of years (n) can be slightly more complex. You can rearrange the equation to solve for r. Given that the target amount is $11,000, the current value is $9,800, and the time frame is 2 years, we set A to $11,000, P to $9,800, and n to 2. The new formula would be (A/P)^(1/n) - 1 = r, which results in the required annual return rate.
Plugging in the values, the formula for this situation is (11,000 / 9,800)^(1/2) - 1. This will give you the annual return rate needed for the investments to reach $11,000 in two years.
Note: Calculations require precision and the use of a calculator or financial software to get the exact rate needed.