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?

Answer 1

First we need to find the future value for $1,000;

FVA5 = Annuity x [{(1 + r)ⁿ - 1} / r]

= $1,000 x [{1.0635⁵ - 1} / 0.0635]

= $1,000 x [0.3605 / 0.0635] = $1,000 x 5.6766 = $5,676.62

FV_1,00018 = FVA5 x (1 + r)^{(18 - 5)}

= $5,676.62 x 1.0635¹³ = $5,676.62 x 2.2263 = $12,637.97

Now, we need to find the future value for $2,000;

FVA10 = Annuity x [{(1 + r)ⁿ - 1} / r]

= $2,000 x [{1.0635⁵ - 1} / 0.0635]

= $2,000 x [0.3605 / 0.0635] = $2,000 x 5.6766 = $11,353.24

FV_2,00018 = FVA10 x (1 + r)^{(18 - 10)}

= $11,353.24 x 1.0635⁸ = $5,676.62 x 1.6364 = $18,578.89

Now, we need to find the future value for $3,000;

FVA18 = Annuity x [{(1 + r)ⁿ - 1} / r]

= $3,000 x [{1.0635⁸ - 1} / 0.0635]

= $3,000 x [0.6364 / 0.0635] = $3,000 x 10.0227 = $30,068.01

Amount they will have accumulated for Sally's college fund

= FV_1,00018 + FV_2,00018 + FVA_3,00018

= $12,637.97 + $18,578.89 + $30,068.01 = $61,284.86