# Annuity

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Annuities, Sinking Funds, and Amortization Math Analysis and Discrete Math – Sections 5.3 and 5.4 I. Warm-Up Problem Previously, we have computed the future value of an investment when a fixed amount of money is deposited in an account that pays interest compounded periodically. Often, however, people do not deposit money and then sit back and watch it grow. Rather, money is invested in small amounts at periodic intervals. Consider these problems: 1. Chrissy deposits \$200 each year into a savings account that has an annual interest rate of 8% compounded annually. How much money will Chrissy have in her account after three years? Hint: Make up a table of how much she has in her account by year. 2. Ben saves \$50 per month in a credit…show more content…
Problem 3: Paying off Bonds The state has \$5,000,000 worth of bonds that are due in 20 years. A sinking fund is established to pay off the debt. If the state can earn 10% annual interest compounded annually, what is the annual sinking fund deposit needed? Problem 4: Managing a Condo The Crown Colony Association is required by law to set aside funds to replace its roof. It is estimated that the roof will need to be replaced in 20 years at a cost of \$180,000. The condo can invest in treasuries yielding 6% paid semiannually. If the condo invests in the treasuries, what semiannual payment is required to have the funds to replace the roof in 20 years? ***Problem 5: Time Needed for a Million Dollars If Josh deposits \$10,000 every year in an account paying 8% compounded annually, how long will it take him to accumulate \$1,000,000? Homework: 5.3: #1-25 every other odd, 35-36 Page 4 of 7 V. Present Value of an Annuity Definition: The present value of an annuity is the amount of money needed now so that if it is invested at i percent, n equal dollar amounts can be withdrawn without any money left over. Problem: College Tuition Jessica's parents will be paying her college tuition of \$20,000 per year for 4 years. If they currently have the money invested at 6% compounded annually, how much money do they need to have in the account to pay the tuition? (Assume that "now" is the beginning of the year and the payment will be made at the