business Math-MTH 170

Business Math-MTH 170 Group Case Study Summer 2022 1. Thomas, a 25-year-old college graduate, wishes to retire at age 65. To supplement other sources of retirement income, he can deposit $167 each month into a tax-deferred individual retirement arrangement (IRA). The IRA will earn a 5% monthly compounded return over the next 40 years. If he makes annual end-of-month $167 deposits into the IRA, how much will he have accumulated by the end of his sixty-fth year? 2. While vacationing in Florida, John Kelley saw the vacation home of his dreams. It was listed with a sale price 0f$200,000. The only catch is that John is 40 years old and plans to continue working until he is 65. Still, he believes that prices generally increase at the overall rate of ination. John believes that he can earn 9% compounded semi annually after taxes on his investments. He is willing to invest a xed amount at the end of each of the next 25 years to fund the cash purchase of such a house (one that can be purchased today for $200,000) when he retires. a. Ination is expected to average 5% per year for the next 25 years. What will John's dream house cost when he retires? b. How much must John invest at the end of each of the next 25 years to have the cash purchase price of the house when he retires? c. If John invests at the beginning instead of at the end of each of the next 25 years, how much must he invest each year? 3. A grandmother wants to provide an annuity of $3000 payable at the end of every six months during the three years that her grandson attends college. What single deposit must she make today that will fmance the annuity, if the grandson will start college in 15 years? Assume she can invest the money at 2.85% compounded semi-annually for the first seven years, and then at 3.0% compounded semi-annually for the next 11 years. 4. Tina purchases a new computer by financing it on the \"no payment until next year\" plan. The cash price of the computer is $1384. The financing agreement requires equal payments every month for two years. If the rst payment of $95$95 is due at the beginning of the month starting one year after the date of purchase, and interest is 28.8% compounded monthly during the rst year, what is the monthly compounded nominal interest rate for the following two years