1. Ordinary Annuities, Sinking Funds, and Retirement Investments
Section 10.6
Ordinary Annuities, Sinking Funds, and Retirement Investments
Annuities and sinking funds are an important part of a long-term investment strategy.

2. Annuity
Annuity: An account into which, or out of which, a sequence of scheduled payments is made.
Ordinary Annuity (fixed annuity): Equal payments are made at regular intervals, with the interest compounded at the end of each interval and with a fixed interest rate for each compounding period.
The accumulated amount, A, of an ordinary annuity with payments of p dollars made n times per year, for t years, at interest rate, r, compounded at the end of each payment period is given by the formula

3. Example 1: Using the Ordinary Annuity Formula
Bill and Megan are depositing $250 each quarter in an ordinary annuity that pays 4% interest compounded quarterly. Determine the accumulated amount in this annuity after 35 years.
p = $250, r = 0.04, n = 4, t = 35.
There will be about $75, in Bill and Megan’s
annuity after 35 years

4. Ordinary Annuity Versus Sinking Fund
An ordinary annuity is used when you wish to determine the accumulated amount obtained over n years when you contribute a fixed amount each period.
A sinking fund is used when you wish to determine how much money an investor must invest each period to reach an accumulated amount at a specific time.

5. Sinking Fund Payment Formula
A sinking fund is a type of annuity in which the goal is to save a specific amount of money in a specific amount of time.
In the formula, p is the payment needed to reach the accumulated amount, A. Payments are made n times per year, for t years, into a sinking fund with interest rate r, compounded n times per year.

6. Example 2: Using the Sinking Fund Payment Formula
The Burnettes would like to have $55,000 in 10 years to purchase a travel trailer for camping. The Burnettes decide to invest monthly in a sinking fund that pays 3.3% interest compounded monthly. How much should the Burnettes invest in the sinking fund each month to accumulate $55,000 in 10 years?
A = $55,000, r = 0.033, n = 12, t = 10
Round our answer up to $ to ensure that the Burnettes reach their goal of $55,000.

7. Other Types of Annuities
Variable Annuity: An annuity that is invested in stocks, bonds, mutual funds, or other investments that do not provide a guaranteed interest rate.
Immediate Annuity: Annuity that is established with a lump sum of money for the purpose of providing the investor with regular, usually monthly, payments for the rest of the investor’s life. In exchange for giving the investment company a lump sum of money, the investor is guaranteed to receive a monthly income for the duration of the investor’s life.
Individual Retirement Accounts(IRAs): Accounts where the individuals may invest up to a certain amount of money each year for the purpose of saving for retirement.