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ANNUITIES




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Finance Notes Annuities Page 1 of 8 ANNUITIES Objectives: After completing this section, you should be able to do the following: • Calculate the future value of an ordinary annuity. • Calculate the amount of interest earned in an ordinary annuity. • Calculate the total contributions to an ordinary annuity. • Calculate monthly payments that will produce a given future value. Vocabulary: As you read, you should be looking for the following vocabulary words and their definitions: • ordinary annuity • simple annuity • Christmas club • tax-deferred annuity (TDA) • present value of an annuity Formulas: You should be looking for the following formulas as you read: • future value of an ordinary annuity • total contribution to an annuity • interest earned on an annuity • present value of an annuity An annuity is defined by merriam-webster.com as “a sum of money payable yearly or at other regular intervals”. Wikipedia defines an annuity as “any recurring periodic series of payment”. Some examples of annuities are regular payments into a savings account, monthly mortgage payments, regular insurance payments, etc. Annuities can be classified by when the payments are made. Annuities whose payments are made at the end of the period are called ordinary annuities. Annuities whose payments are made at the beginning of the period are called annuity-due. In this class we will only work with ordinary annuities. ordinary annuity annuity due Finance Notes Annuities Page 2 of 8 We will need to be able to calculate the future value of our annuities. In order to do this we will need a formula to calculate future value if we know the amount of the payment, the interest rate and compounding period, and the number of payments. NOTE: The payment period and the compounding period will always match in our problems. Annuities which have the same payment and compounding period are called simple annuities. Example 1: Find the future value of an ordinary annuity with $150 monthly payments at 6¼% annual interest for 12 years. Solution: For this problem we are given payment amount ($150), the interest rate (.0625 in decimal form), the compounding period (monthly or 12 periods per year), and finally the time (12 years). We plug each of these into the appropriate spot in the formula       −       + = n r n r pymt FV t n 1 1 * . This will give us Future Value of an Ordinary Annuity       −       + = n r n r pymt FV t n 1 1 * FV = future value pymt = payment amount r = interest rate in decimal form n = number of compounding periods in one year t = time in years simple annuity Finance Notes Annuities Page 3 of 8 04651 . 32051 12 0625 . 1 12 0625 . 1 150 12 * 12 =     ...





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