Answer:
$4,102.57
Explanation:
we must first calculate the future costs of college:
cost of college year 1 = $16,200 x (1 + 2%)¹⁰ = $19,747.71
cost of college year 2 = $19,747.71 x 1.02 = $20,142.66
cost of college year 3 = $20,142.66 x 1.02 = $20,545.51
cost of college year 4 = $20,545.51 x 1.02 = $20,956.42
in order to determine how much money does the family need to have before college starts we must discount the cost of college by 7.5%:
PV cost of college year 1 = $19,747.71
PV cost of college year 2 = 20,142.66 / 1.075 = $18,737.36
PV cost of college year 3 = $20,545.51 / 1.075² = $17,778.70
PV cost of college year 4 = $20,956.42 / 1.075³ = $16,869.09
total = $73,132.86
the future value of the grandmother's deposits:
$13,000 x (1 + 7.5%)¹⁴ = $35,781.77
$2,900 x (1 + 7.5%)¹² = $6,907.16
total = $42,688.93
that means that you will need to save $73,132.86 - $42,688.93 = $30,443.93 by the time your child turns 18
you will make 4 deposits and their future value will be:
deposit x 1.075¹⁰ = 2.0610D
deposit x 1.075⁹ = 1.9172D
deposit x 1.075⁸ = 1.7835D
deposit x 1.075⁷ = 1.6590D
total = 7.4207D
yearly deposit = $30,443.93 / 7.4207 = $4,102.57
