finance

Time Value of Money – Case #1

Show your work including any intermediate steps. Some partial credit awarded but must complete the problem.

Problem #1

A father is now planning a savings program to put his daughter through college. She is 13 and plans to enroll in college in 5 years, and she should graduate 4 years later. Currently, the annual cost for college is $15,000 and is expected to increase 4% each year. The college requires that the costs be paid at the start (hint: beginning) of each year. The child now has $7,500 saved for college in an account and is expected to have a return of 6% annually. The father will make six equal payments starting today and the sixth on the day she starts college and make no more additional payments. How much must each of the payments be to fully fund the college cost?

Problem #2

Brian is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power throughout his retirement as $40,000 today. His retirement income will begin the day he retires, 10 years from today, at which time he will receive his first payment and then 24 additional payments at the beginning of the next 24 years. 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. How much must he save each of the next 10 years (assuming end of the year payments) to meet his retirement goal?

Problem #3

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%.

a. For the 30th payment how much of the payment is payment of principle vs interest.

b. The homeowner was expecting to use an annual bonus to be made as an additional payment of $5,000 every 12th payment in addition to the normal loan payment. The homeowner’s goal was to reduce the overall amount of interest paid on the loan.

a. For the 30th payment how much is now the payment of principle vs. interest.

b. How many months will it now take to pay off the loan?