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CHAPTER 4: Annuities 149 B. any 6. 7. Sinking Funds with Loans A company borrowed $40,000 for 3 years at 6% compounded daily. It will not make payments on this loan prior to maturity. Find (a) the total future value they will need to accumulate to pay off this debt, and (b) the quarterly sinking fund payment needed to accumulate this maturity value, assuming a 5% rate. Jason's uncle loaned him $37,500 to help him start a landscaping business. They agreed that Jason would pay off the entire loan plus 31% annually compounded interest in 3 years, and that in the meantime he would make monthly deposits into a bank account to make sure that he has the amount needed when the loan comes due. The bank account will pay 3%. (a) Find the total amount Jason will need to repay the loan. (b) How much should each of his monthly deposits be? C. Sinking Funds and Retirement Planning 8. Astrid figures that in the next 20 years she needs to build up a balance of $500,000 in a retirement account she has just opened. Deposits into this account will be made by deductions from her biweekly paychecks (26 times per year). If her account can earn 8.4%, how much should each deposit be? 9. Redit hopes to build up an account value of $1,600,000 over the next 40 years in an account that he thinks will earn 11.27%. Under these assumptions how much should he invest each month? (a) Find the total amount (b) How much should each of his monthly Sinking Funds and Retirement Planning Redit hopes to build up an account value of $1,600,000 over the next 40 years in an aschunt that he thinks will earn 11.27%. Under these assumptions how much should he invest Astrid figures that in the next 20 years she needs to build up a balance of $500,000 in a retirement account she has just opened. Deposits into this account will be made by deductions from her biweekly paychecks (26 times per year). If her account can earn 8.4%, how much should sure it has the money needed to repay the loan when it comes due, the count in making deposits Kinzua County borrowed $4,250,000 at an effective rate of 4.25% for 5 years. To make . 8. each deposit be? 9. each month? D. Grab Bag 10. The business manager of the Rock City Central School District commented at a school board meeting that in Zvears the district will have a loan coming due that will require $996,423 to pay. He recommended that the district should prepare for this payment by setting funds aside each year in an account paying 3.09% to build up the needed balance. According to his plan, how much should each payment be? 11. I just borrowed $30,000 which I will have to pay off in 5 years together with interest. Interest accumulates at an effective rate of 10.33%. (a) How much in total will I need to pay off this loan when it comes due? (b) How much should I deposit to a sinking fund each month to be able to pay off this loan, assuming that my account pays 3.68% compounded monthly? 12. Paul has nothing in his savings account but he wants to have $8,000 in it 1 now. If the account pays 26%, how much should he deposit each week? 13 How much would you need to deposit each week into an account earning 8.5% in order to have $1,000,000 in 40 years? 14. assuming a 6.1% interest rate, 15. into a sinking fund at the beginning of each quarto (a) How much will the year from Find the monthly sinking fund payment needed to accumulate $5,000 in 3 years #10 Complete the problem in the text then this additional part. Part b Find how much interest the district will end up earning. Because they are making payments into a sinking fund rather than paying one lump sum after 7 years, they will earn interest on their annual payments. Although the interest will not be kept by the District but rather used to pay their debt, it is still earned interest. How much interest will they earn? & Non-textbook 1. Suppose that your goal is to have $1,000,000 in your retirement account when you retire. You don't have a fixed idea of when you will retire, but decide to save $100 of each weekly paycheck automatically deducted and deposited in the retirement account. The account earns 6.5% annual interest, compounded weekly. In about how many years will the value of the investment reach $1 million? Show your work and round your answer off to the nearest year