Final answer:
This question involves college-level financial mathematics, focusing on annuities and compound interest, valuable for saving long-term for goals like opening a tutoring center. The future value of an annuity and compound interest calculations require specific data on payments and interest rates.
Step-by-step explanation:
The subject matter presented in the question revolves around financial planning, specifically concerning the calculation of annuities and compound interest. These concepts are part of the financial mathematics curriculum often taught in college-level business or finance courses. An annuity is a series of equal payments made at regular intervals, and it can be used as a savings strategy for long-term financial goals such as opening a tutoring center. The formula for the future value of an annuity takes into account the amount of each payment, the interest rate, and the number of payments made over time.
To calculate the future value of the annuity that Latoya purchases, one would need to use the formula for the future value of an annuity: FV = Pmt * [((1 + r)^n - 1) / r], where FV is the future value of the annuity, Pmt is the annual payment, r is the interest rate, and n is the number of years the payments are made. It would be necessary to have the specific values for the yearly payment amount and the interest rate to perform the calculation.
Similarly, the concept of compound interest is crucial to understanding how investments grow over time. Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods. The compound interest formula is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time in years.