Tuition at the State University is currently $11,000 a year and is expected to rise by 7% every year. Beth has 6 years till she starts college because she is presently 12 years old. The account earns 4% interest per year, compounded.
Mary has agreed to pay half of the school fees ($11,000/2), which remains the principle sum.
The following are the fees that Mary is expected to pay each year for Beth's college education:
$39,343.1 for the first year of college = $5,500*((1.07)6 - 1)/0.07
For the second year of college = $5,500*((1.07)7 - 1)/0.07 = $47,597.12
For the third year of college = $5,500*((1.07)8 - 1)/0.07 = $56,428.91
For the fourth year of college = $5,500*((1.07)9 - 1)/0.07 = $65,878.94
Thus, the total fee that Mary is expected to pay towards Beth's College Education is
= $39,343.1 + $47,597.12 + $56,428.91 + $65,878.94 = $209,248.07
Now Mary intends to start making savings deposits to be able to cover the college fees. This is expected to earn interest rate of 4% for the six years before Beth starts her college education.
The formula for amount in instance of compound interest is A= P*[(1+i) ^n -1]/I,
where A is the amount accumulated after n years, P - the principal, I - annual interest rates, n - number of periods.
From the data we've computed, P is the amount of deposit Mary needs to make.
To have, $209,248.07 = P* [(1.04) ^6 -1] / 0.04 = $31,546.64
Hence, Mary should deposit $31,546.64 each year for the next six years in order to be able to pay the half portion of Beth's college fees.
