Final answer:
To find the principal Tremayne must invest to have $50,000 in 15 years at 4% interest compounded monthly, we use the future value compound interest formula. Substituting the values, Tremayne can calculate the initial amount to invest in his daughter's college education.
Step-by-step explanation:
Tremayne is looking into the future value of an investment and how much he needs to invest now to reach his goal of $50,000 in 15 years for his daughter's college education, considering a 4% interest rate compounded monthly.
To find the principal (P), we use the formula for the future value of a compound interest account: P = A / (1 + r/n)n*t, where A is the amount desired in the future, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
To achieve his goal, Tremayne would do the following calculation:
Principal P = $50,000 / (1 + 0.04/12)12*15
After inputting the values and calculating, Tremayne will find the initial amount he must deposit to have $50,000 in 15 years.