A Lifetime of Savings
For 70 years, Oseola McCarty earned a living washing and ironing other people’s clothing in Hattiesburg, Mississippi. Although she did not earn much money, she budgeted her money wisely, lived within her means, and began saving at a very young age. Before she died, she drew worldwide attention by donating \$150,000 to the University of Southern Mississippi for a scholarship fund in her name. The fact that Ms. McCarty was able to save so much money and generously gave it away is an inspiration to many others. She was honored with the Presidential Citizens Medal for her generosity. How did she do it?
Let’s assume that she saved the same amount at the end of each year and invested it in a savings account earning 5% per year compounded annually. (When you contribute the same amount each year to an account it is called an annuity.) How much do you think Ms. McCarty would have to save each year in order to accumulate \$150,000 over a 70year period?
 Before we figure it out, take a guess.
 \$100
 \$250
 \$500
 \$1,000
 \$2,000
 Suppose Ms. McCarty saved \$100 and then deposited it at the end of the year in an account that earns 5% interest, compounded annually.
 How much will it be worth at the end of the second year? At the end of the third year? At the end of the 70th year?
 Write an expression that represents the value of an investment of $C$ dollars after 70 years. Assume as above that it is deposited at the end of the first year in an account that earns 5% interest, compounded annually.
 Now suppose Ms. McCarty saved another \$100 in the second year and then deposited it at the end of that year in her account.
 How much will it be worth at the end of the third year? At the end of the fourth year? At the end of the 70th year?
 Write an expression that represents the value of an investment of $C$ dollars after 69 years.
 Suppose Ms. McCarty saved \$100 each and every year for 70 years. Each time, she deposited it in her account at the end of the year.
 How much would she have saved? What would it be worth at the end of 70 years?
 Write an expression that represents the value of an investment of $C$ dollars deposited each year for 70 years. Assume as above that it is always deposited at the end of the year in an account that earns 5% interest, compounded annually.
 Had she saved \$1,000 a year, how much would she have had after 70 years under the same conditions?
 How much would she have to save each year in order to accumulate \$150,000 after 70 years? How does this compare to your guess? Are your surprised by the answer?

The future value $FV$ of an annuity is the total value of the annuity after a certain number of years. The formula for the future value of an annuity is shown below.
$$ {FV} = C \cdot \left[ \frac{(1+ r)^t  1}{r} \right] $$Based on the work you did above, what is the meaning of $C$ in this context? What is the meaning of $r$ in this context? What is the meaning of $t$ in this context?