1. Suppose today is July 1, 2010, and you deposit KD 3,000 into an account today. Then you deposit KD 1,500 into the same account each July 1, beginning in 2011 and continuing until the last KD 1,500 deposit is made on July 1, 2016. Also, assume you withdraw KD 5,000 on July 1, 2018. Assuming a 7% annual compound interest rate, what will be the balance in the account at the end of July 1, 2020? (hint: find the present value for CFs then the future value for lump sum)

1. Sara is considering taking early retirement, having saved KD 200,000. She desires to determine how many years the savings will last if KD 15,000 per year is withdrawn at the end of each year. Sara feels the savings can earn 5% per year.

1. Bader has just turned 30 years old. He has currently accumulated KD 35,000 toward his planned retirement at age 60. He wants to accumulate enough money over the next 30 years to provide for a 20-year retirement annuity of KD 100,000 at the beginning of each year starting at with his 60th He plans to save KD 5,000 at the end of each of the next 10 years. What equal amount must he save at the end of years 11 through 30 to meet this objective? The interest rate for the first 10 years will be 4%. After that time, the interest rate is expected to be 8%.

1. Kuwait Investments has offered you the following investment opportunity:
• KD 10,000 at the end of each year for the first 5 years, plus
• KD 5,000 at the end of each year from years 6 through 10, plus
• KD 4,000 at the end of each year from years 11 through 20.
1. How much would you be willing to pay for this investment if you required a 8% rate of return?
2. If the payments were received at the beginning of each year, what would you be willing to pay for this investment?

1. Jamal has just turned 26 years of age. In 4 years he expects to start saving for retirement. He wishes to be able to withdraw KD 100,000 per year during the first 10 years of retirement (the first withdrawal coming on his 61st birthday) and KD 150,000 during the next 10 years of retirement. As a precaution against unexpected longevity, he would like to have a net worth of KD 500,000 after the withdrawal on his 80th He expects the return on his investments to 5%. What equal annual amount must Jamal save at the end of each year (the first deposit will occur on his 31st birthday and the last deposit will occur on his 60th birthday) to meet these retirement goals?
2. This year’s operating costs were down \$100,000, a decrease directly attributable to the \$520,000 investment in the automated materials handling system put in place at the beginning of the year.
1. If this level of annual savings continues for five more years, resulting in six total years of annual savings, what compounded annual rate of return will that represent?
2. How much is the net present value this investment if the required rate of return is 10%?
3. If these annual savings continue for nine more years, for a total of 15 years of annual savings, what compounded annual rate of return will that represent?
4. How much is the net present value this investment if the required rate of return is 10%?

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