Mary wants to 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?

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

a ab

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