1. Two brothers each open IRAs in 2009 and plan to invest S3,000 per year for the next 30 years John makes his first deposit on January 1, 2009, and will make all future deposits on the first day of the year. Bill makes his first deposit on December 31, 2009, and will continue to make his annual deposits on the last day of each year. At the end of 30 years, How much the difference in the value of the IRAs (rounded to the nearest dollar), assuming an interest rate of 7% per year will be?
2. Bill borrowed $100,000 today that he must repay in 15 annual end-of-year installments of $10,000. What annual interest rate is Bill paying on his loan?
3. You deposit $5,000 per year at the end of each of the next 25 years into an account that pays 8% compounded annually. How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The first withdrawal is made at the end of the first year in the 20-year period.)
4. A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns 7.5% interest per year, starting on his first birthday. How much would you need to invest each year (rounded to the nearest dollar) to accumulate a million for your child by the time he is 35 years old?
5. You have contracted to buy a house for $250,000, paying $30,000 down and taking out a fully amortizing loan for the balance, at a 5.7% annual rate for 30 years. What will your monthly payment be if they make equal monthly installments over the next 30 years (to the nearest dollar)?
6. Cindy wants $2.5 million for her retirement at age 65. Cindy is 25 years old today and plans to deposit equal amounts each year starting on her 26th birthday and ending on her 65th birthday If her investments earn 6% per year, how much must each deposit be?
7. An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven years. What is the present value of this investment if our opportunity rate is 5%?