The accumulated value of a savings account based on regular periodic payments can be determined from the annuity due equation, A = -1(1 + 0"- U- i In this equation, A is the amount in the account, P is the amount regularly deposited, and / is the rale ofinterest per period for the n deposit periods. An engineer would like to have a savings account valued at $750,000 upon retirement in 20 years and can afford to put $1500 per month toward this goal. What is the minimal interest rate at which this amount can be invested, assuming that the interest is compounded monthly?
L29 - 2 To Solve an Optimization Problem 1. Read the problem carefully to determine the quantity Q that you are trying to optimize, and the conditions involved. 2. Draw a sketch if possible and assign symbols to known and unknown quantities. 3. Find the function representing the quantity to be optimized (Q): the Primary Function (Object Function) 4. If necessary, ﬁnd an equation relating the variables involved (the Constraint)a dw eheriya function as the function of a single variable. 5. Use calculus to ﬁnd the desired maximum or minimum; check your result. You can use the ﬁrst or second derivative test, or the extreme value theorem if the domain is a closed interval.