10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 649 14. Weekly payment with a 6.5% interest rate compounded weekly for 30 years to accumulate $800,000 $166.11 15. Monthly payments with a 6% interest rate compounded monthly for 35 years to accumulate $250,000 $175.48 16. Quarterly payments with a 10% interest rate compounded quarterly for 40 years to accumulate $1,000,000 $490.41 Problem Solving In Exercises 17–20, round all answers to the nearest cent. 17. Retirement Savings To save for retirement Simon invests $150 each month in an ordinary annuity with a 3.3% interest rate compounded monthly. Determine the accumulated amount in Simon’s annuity after 40 years. $149,271.58 18. Starting a Business To save money to start a new business, Sandra invests $200 each quarter in an ordinary annuity with a 5% interest rate compounded quarterly. Determine the accumulated amount in Sandra’s annuity after 20 years. $27,223.76 19. Saving for Graduate School To save for graduate school, Claire invests $1500 semiannually in an ordinary annuity with a 6% interest rate compounded semiannually. Determine the accumulated amount in Claire’s annuity after 10 years. $40,305.56 20. Grandchild’s College Expenses To save for their grandchildren’s college expenses, Ken and Laura invest $500 each month in an ordinary annuity with a 6% interest rate compounded monthly. Determine the accumulated amount in the their annuity after 18 years. $193,676.60 In Exercises 21–24, round all answers up to the next cent. 21. Saving for a New Motorcycle Nick would like to have $24,000 to buy a new motorcycle in 6 years. To accumulate $24,000 in 6 years, how much should Nick invest monthly in a sinking fund with a 7.5% interest rate compounded monthly? $264.97 22. Campaign Fund-Raising Ashley would like to run for Congress in 10 years and would like to have $500,000 to spend on campaign expenses. How much should she invest monthly in a sinking fund with a 6% interest rate compounded monthly to accumulate $500,000 in 10 years? $3051.03 23. Becoming a Millionaire Becky would like to be a millionaire in 20 years. How much would she need to invest quarterly in a sinking fund paying an 8% interest rate compounded quarterly to accumulate $1,000,000 in 20 years? $5160.71 24. Repaying a Debt The city of Raleigh, North Carolina wishes to repay a debt of $25,000,000 in 50 years. How much should the city invest semiannually in a sinking fund paying a 7.5% interest rate compounded semiannually to accumulate $25,000,000 in 50 years? $24,223.66 m Raleigh, North Carolina Challenge Problems/Group Activities 25. Don’t Wait to Invest The purpose of this exercise is to demonstrate that it is much more beneficial to begin to invest for retirement early than it is to wait. We will compare the investments of two investors, Alberto and Zachary. Alberto begins to invest immediately after graduating from college, whereas Zachary waits 10 years to begin investing. For the purposes of this demonstration, we will assume that the interest rate remains the same over the entire period of time. a) From age 25 to 35, Alberto invests $100 per month in an annuity that pays a 12% interest rate compounded monthly. Determine the accumulated amount in Alberto’s annuity after 10 years. $23,003.87 b) At age 35, Alberto stops making monthly payments into his annuity, but he takes the money he accumulated in his annuity and invests it in a savings account with an interest rate of 12% compounded monthly. Using the compound interest formula A p r n 1 , n t ( ) = ⎛ + ⎝⎜ ⎞ ⎠⎟ ⋅ determine the amount Alberto has in his savings account 30 years later when he retires at age 65. $826,980.88 c) From age 35 to 65, Zachary invests $100 per month in an annuity that pays 12% interest compounded monthly. Determine the accumulated amount in Zachary’s annuity after 30 years. $349,496.41 d) Determine the total amount Alberto invested during the 10 years from age 25 to 35. $12,000 e) Determine the total amount Zachary invested during the 30 years from age 35 to 65. $36,000 f) Which investor has more money from the investments described here upon retirement? Alberto Spiroview Inc/Shutterstock ESB Professional/Shutterstock
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