Sinking Fund and Annuity

A businesswoman, expecting the birth of a girl, wants to create a savings account that will pay for her child’s college costs in 18 years. She will do this by depositing equal amounts from her paycheck every month (with the first deposit made on the day of the child’s birth) into an account that pays 0.5% interest per month. Then the month prior to the child’s 18th birthday she will make her last deposit into the account, and, on her birthday the next month, the child will begin withdrawing $2000 from the account each month for 4 years to pay for college. The woman wishes to determine how much she should deposit each month for the 18 years.

1. Describe how to model this situation using difference equations. Explain your logic and include the relevant equations.

2. Use Excel and trial and error to determine what her monthly deposit should be.

3. Suppose the child wins a contest and a deposit of $5000 is added to the account (along with the monthly deposit) on her 10th birthday (month 121). The businesswoman wants to adjust the amount withdrawn from her check to account for the deposit. What amount should be withdrawn from her paycheck for the remaining 8 years?