Question

1. A couple with a newborn daughter wants to save for their child’s college expenses in advance. The couple can establish a college fund that pays 7% interest compounded daily. Assuming that the child enters college at age 18, the parents estimate that an amount of $22500 per year will be required to support the child’s college expenses for four years of education. Determine the equal annual amounts the couple must save until they send their child to college. Assume that the first deposit will be made on the child’s first birthday and the last deposit on the child’s 18^th birthday. College payments happen at the beginning of every year during the four years of education. The first withdrawal will be made at the beginning of the freshman year, which is the child’s 18^th birthday. (round your final answer to 1 decimal point)

Answer 1

Assuming 365 days in 1 yr

Effective interest rate = (1+0.07 / 365)^365 - 1 = 0.07250098 ~ 7.25%

Present value of college education cost at 18th birthday = 22500 + 22500 * (P/A,7.25%,3)

= 22500 + 22500 *((1 + 0.0725)^3-1)/(0.0725*(1 + 0.0725)^3)

= 22500 + 22500 *((1.0725)^3-1)/(0.0725*(1.0725)^3)

= 22500 + 22500 *2.612375

= 81278.44

Annual investment required = 81278.44 * (A/F,7.25%,18)

= 81278.44 *0.0725 / ((1 + 0.0725)^18-1)

= 81278.44 *0.0725 / ((1.0725)^18-1)

= 81278.44 *0.028714

= 2333.8