Final answer:
The amount of money after t years when $10,000 is compounded quarterly at 12% interest is calculated using the compound interest formula: $10,000 × (1 + 0.12/4)^4t.
Step-by-step explanation:
The correct expression for the amount of money after t years when $10,000 is compounded quarterly at 12% interest is given by the formula for compound interest: A = P(1 + r/n)nt. Here, A is the amount of money accumulated after t years, including interest, P is the principal amount ($10,000), r is the annual nominal interest rate (12%, or 0.12 as a decimal), n is the number of times that interest is compounded per year (quarterly compounding means n = 4), and t is the number of years.
The correct formula, when plugged with the given values, will therefore be: $10,000 × (1 + 0.12/4)4t
It is important to divide the annual rate by the number of compounding periods per year and then raise this to the power of the total number of compounding periods (n times t).