Question

At the end of each year for the first 5 years, Cecil and Norma DeMille plan to contribute $1,000 to their daughter Sally's college fund. For the next 5 years they will contribute $2,000 at the end of each year, and then increase that amount to $3,000 until she turns 18 and is ready for college. What amount will they have accumulated for Sally's college fund if the account pays 6.35% annually?

Please be very thorough with work and provide the specific formula used.

Answer 1

	Accumulated value	Accumulated value left in account(no further contribution) for remaining years to maturity (till18 years)	Future value at end of year 18
For first 5 years	FVA6.35%,5 *Amount 5.67662*1000 5676.62	18-5=13 years	FVF6.35%,13*Accumulated value 2.22632*5676.62 12637.97
For next 5 years	FVA 6.35%,5*Amount 5.67662*2000 11353.24	18-5-5=8 years	FVF6.35%,8*Accumulated value 1.63644*11353.24 18578.90
For next 8 years   [18-5-5]	FVA6.35%,8*Amount 10.02267*3000 30068.01	0	30068.01
		Total value	61284.88

Total value accumulated : 61284.88

**Find future value factor using the formula : 1/(1+i)^n or using the financial calculator

**find future value annuity factor using the formula :[(1+i)^1+(1+i)^2+(1+i)^3+...(1+i)^n-1] or using financial calculator or from future value annuity table]

For first 5years annuity factor = [1+(1+i)^1+(1+i)^2+....(1+i)^4]

for 8 years annuity factor = [1+(1+i)^1+(1+i)^2+....+(1+i)^7]