Final answer:
After one year, John has $1,140 more than Steven. This was calculated by applying the compound interest formula to their respective investments and then comparing the results.
Step-by-step explanation:
The student's question is about compound interest and how it affects the growth of two different investments over a year. To compare Steven's and John's investments, we need to calculate the amount each brother will have after one year using the formula A = P(1 + r)^n, where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and n is the number of times the interest is compounded per year (which in this case is once since it's annually).
Steven's Investment:
Steven invests $30,000 at a 2.3% annual return.
A = 30,000(1 + 0.023)
A = 30,000(1.023)
A = $30,690
John's Investment:
John invests $30,000 at a 6.1% annual return.
A = 30,000(1 + 0.061)
A = 30,000(1.061)
A = $31,830
To find out how much more money John has than Steven after one year, we subtract Steven's total from John's:
$31,830 - $30,690 = $1,140
Therefore, the answer is (c) $1,410