Problem #1 (Under the Lights)
A local youth baseball league has acquired through a gift significant land to build new ball fields. They are planning ahead and would like to eventually install lights at these fields. They plan on installing these new lights over a 3 year period starting 3 years from now and would like to do 3 fundraisers to fully fund it before the new fields and lights can be installed. Additional fund raisers for the lighting project are not expected to be required.
New lights would cost $25,000 for each ball field today but prices are expected to increase 2% per year. They currently have $10,000 saved and allocated to this project. They are planning to have fundraisers now and at the beginning of each year for the next 2 years and would like to fully fund the project before installation of the lights for the first ball field.
Assumptions: Project is fully funded 3 years from today at the time of the first payment for the first set of lights for the first ball field. The second and third installation of lights will happen at the beginning of each of the years subsequent to the first year the lights are installed. Deposits from fund raisers are made today and at the beginning of year 2 and year 3. Assume that each fund raiser will raise an equal amount of money that can be allocated to the lighting project. Assume that money invested will earn 6% interest.
How much must each of the fund raising events raise to fully fund the project?
How would your answer be different if the fund raisers happened at the end of each of the 3 years and not at the beginning?
Problem #2 (Retirement Savings)
Danny is 30 years old and has accumulated some retirement savings but he wants to be more aggressive. He is targeting to retire when he is 55. The ‘expected life expectancy’ charts indicate that he would live to be 90 years old. He has $100,000 in a retirement account today. He wants a fixed retirement income that has the same purchasing power throughout his retirement as $40,000 today. He does not expect to make retirement contributions once he retires so the account must have accumulated enough to fully fund retirement.
His retirement income will begin the day he retires at which time he will receive his first payment. Subsequent payments will be made at the beginning of each year until he is 90 and receives his last payment.
Annual inflation is expected to be 1%. He currently has $100,000 saved, and he expects to earn 8% annually on his savings both before and after he retires. Assume that there are no tax implications. How much must he save each year (assuming end of the year payments) to meet his retirement goal?
Problem #3 (Amortization Problem)
A homeowner just bought a house and entered into a 30 year mortgage of $250,000. Set up an amortization schedule for loan to be repaid in equal installments at the end of each month over 30 years (360 payments). The interest rate is 5%.
For the 30^{th} payment how much of the payment is payment of principle vs interest.
The homeowner was expecting to use an annual bonus to be made as an additional payment of $5,000 every 12^{th} payment in addition to the normal loan payment. The homeowner’s goal was to reduce the overall amount of interest paid on the loan.
For the 30^{th} payment how much is now the payment of principle vs. interest.
Subject | Business |
Due By (Pacific Time) | 05/09/2015 09:00 am |
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