Question

Mary wants to help pay for beth's education(her granddaughter). she has decided to pay for  half of the tuition costs, which are now $11,000 per year at state university. tuition is expected to increase at a rate of 7% per year into the foreseeable future and beth just had her 12th birthday. beth plans to start college on her 18th birthday and finish in four years. mary will make a deposit today and continue making deposits each year until beth starts college, and will earn 4% compounded annually on this account. how much must mary's deposit be each year in order to pay half of beth's tuition at the beginning of each school each year?

Answer 1

First, you have to calculate the amount of tuition when the student reaches age 18. Do this by multiplying $11,000 by 1.07 each year from age 12 until it reaches age 18. Thus, 7 times.

At age 18: 16,508

At age 19: 17,664

At age 20: 18,900

At age 21: 20,223

Then, we use this formula:

A = F { i/{[(1+i)^n] - 1}}

where A is the monthly deposit each year, F is the half amount of the tuition each year illustrated in the first part of this solution, n is the number of years lapsed.

At age 18:

A = (16508/2) { 0.04/{[(1+0.04)^6] - 1}} = $1,244.389 deposit for the 1st year

Ate age 19

A = (17664/2) { 0.04/{[(1+0.04)^7] = $1,118 deposit for the 2nd year

At age 20:

A = (18900/2) { 0.04/{[(1+0.04)^8] = $1,025 deposit for the 3rd year

At age 21:

A = (18900/2) { 0.04/{[(1+0.04)^8] = $955 deposit for the 4th year