Part I: Lucky YOU!

When you turned $18,$ you found out that your Great$-$Aunt Mildred started a college fund in your name on the day you were born. Now that college is in sight for you, it is time to find out how much money is in the account.

Great Aunt Mildred's original investment was $$40\mathrm{.}000$ at $7\mathrm{.}0\%.$

$($find the appropriate numbers in the table on the last page$)$

How much money does the account have on your ${18}^{th}$ birthday if it was compounded... annually? $

semi$-$annually? $

quarterly?

$

monthly?

daily?

$

What does it mean to have an account that compounds continuously? Research this and write a few sentences about it$.$ How much money would be in the account had it been compounded continuously?

Spring $2023$

Part II: Bills and Expenses

Your research into the cost of college at the three different types of schools listed below resulted in the following information. These figures represent the direct costs for a full$-$time student taking a load of $12$ semester hours for one semester. Direct costs are those costs associated with tuition, fees, room, and board.

community college,

state college$/$university$,$

private college$/$university$.$

$0\mathrm{.}5,000\mathrm{.}0H$

$\backslash$table$[[$School Name,Tuition,Fees,Room,Board$],[\backslash$table$[[1.$ Northwest$-$Shoals$],[$Community College$]],1596,324,,],[2.$ University of Alabama,$5390,400,4500,2405],[3.$ Samford University,$16624,475,4725,2555]]$

Complete the following table for each of the three schools.

$\backslash$table$[[$School Name,$\backslash$table$[[$Total Annual$],[$Cost of$],[$Tuition$/$Fees$]],\backslash$table$[[$Total Annual$],[$Cost of$],[$Room$/$Board$]],\backslash$table$[[$Total Annual$],[$Cost$]]],[\backslash$table$[[1.$ Northwest$-$Shoals$],[$Community College$]],,,],[2.$ University of Alabama,,,$],[3.$ Samford University,,,$]]$

$2$

Answer the following questions based on the amount in the college fund account when compounded quarterly. Show all work.

For each school, determine if the account will cover tuition$/$fees only for your entire college career. $($Keep in mind that community colleges are $2-$year institutions.$)$

$1.$

$2.$

$3.$

For each $4-$year institution, determine if the account will cover tuition$/$fees plus room$/$board for your entire college career.

$2.$

$3.$

Determine the minimum principal amount that Great$-$Aunt Mildred should have invested so that only your tuition$/$fees for all four years would be covered for Samford University.

Determine the minimum principal amount that Great$-$Aunt Mildred should have invested so that your tuition$/$fees plus room$/$board for all four years would be covered for Samford University.

$3$

Part III: Annuity vs$.$ Single Deposit

Instead of making a single deposit on the day you were born, Great$-$Aunt Mildred decides to make annual deposits into an annuity every year on your birthday. Using the same interest rate as before, how much will she need to deposit each year on your birthday in order to cover the total cost of tuition$/$fees plus room$/$board for four years at Samford University? Show all work below.

$\backslash$table$[[\backslash$table$[[$First Letter of Last$],[$Name$]],\backslash$table$[[$Initial$],[$Investment$]],\backslash$table$[[$Interest$],[$Rate$]]],[A-E,$$$25,000,5\mathrm{.}5\%$