Please help me with the following question (with clear work): A couple with a ne
ID: 1091243 • Letter: P
Question
Please help me with the following question (with clear work):
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% annual interest. Assuming that the child enters college at age 18, the parents estimate that an amount of $40,000 per year (actual dollars) will be required to support the child's expenses for 4 years. Determine the equal 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 last deposit on the child's 18th birthday. The first withdrawal will be made at the beginning of the freshman year, which also is the child's 18th birthday).
Explanation / Answer
If we check an annuity table the factor for an annuity of 40,000 for four years is 3.62432 (at beginning of period, annuity due)
So at the end of 17 years they will need to save 40,000* 3.62432= 144,972.80
To accumulate 144,972.80 in 17 years we check what the future valuefactor for an annuity of 17 years at 7% is. It is 30.8402. So they will need to save 144,972.80/30.8402= 4700.77 per year to accumulate that amount.