Michelle Has Just Received an Inheritance from Her Grandfather's Estate

Essay

Michelle has just received an inheritance from her grandfather's estate. She will be entering college in 3½ years, and wants to immediately purchase three compound-interest investment certificates having the following maturity values and dates: $4,000 at the beginning of her first academic year, $5,000 at the start of her second year, and $6,000 at the beginning of her third year. She can obtain interest rates of 5% compounded semi-annually for any terms between 3 and 5 years, and 5.6% compounded quarterly for terms between 5 and 7 years. What principal amount should she invest in each certificate?