Part 1 (2.5 points): At a recent family gathering, you talk to your Uncle Rick a
ID: 2740771 • Letter: P
Question
Part 1 (2.5 points): At a recent family gathering, you talk to your Uncle Rick about your Fin 200 course. Realizing your expertise, he asks you to do a calculation for him. He has a guaranteed pension that he can take at 50 or wait until he is 60. Assume a 5% discount rate and the following: At 50, he will receive $24,000 per year for life.
At 60, he will receive $36,000 per year for life. Assume life expectancy of 100.
Is it better for him to wait until 60 or begin taking the amount at age 50?
What if the value changes at age 65 to 50% of the benefit ($12,000 and $18,000)?
Part 2 (1 point): You are 22 years old and have graduated college with student loans totaling $60,000. At an 8% interest rate and 15 years, how much is your annual payment; What would happen to your payment if your interest rate was reduced to 4.5%
Part 3 (1.5 point): At 32 you decide to buy a house that costs $400,000. If you have a $100,000 down payment, and mortgage the remaining $300,000. Assuming a 30 year mortgage and an interest rate of 4.5% per year, what is your monthly payment? Assuming this is to be 28% of your monthly salary, what does your annual salary need to be?
Part 4 (1 point): At 42, you decide to put money away for your children’s education and determine that you need $200,000 in ten years. How much do you need to put away each year to achieve this goal?
Part 5 (1 point): At 52, you decide to get serious for retirement and want to save. You realize that you can save $50,000 per year. At a 6% discount rate how much will you have saved in 20 years.
Part 6 (3 points): You salaries in life are as follows (you will need to interpolate between the years for the problem):
Age Salary
22 $50,000
32 $85,000
42 $125,000
52, $175,000
62 $200,000
72 $150,000
How much will you have in your 401k account at age 72 if you allocate 6% of your salary each year since 22, and your company contributes 3% in addition to your contribution? Assume a 6% discount rate.
Also, how much will you have in the account at age 72 if you wait until age 32 to start contributing (you lose the 6% and the company 3% for 10 years)?
Explanation / Answer
Step-1:
At the age of 50 he will receive = $24,000
At the age of 60 he will receive = $36,000
Discount rate = $24,000 * 5% = $1,200
Discount rate = $36,000 * 5% = $1,800
The benefit receive between age of 50 to 60
If he wait 10 more years he will receive the benefit = $12,000.
At the age, between 65 to 50:
His benefit between 50 to 60 = $12,000
Between 50 to 65 = $18,000
Step-2:
Student loan = $60,000
Interest rate = 8%
= $60,000 * 8% = $4,800
=$64,800 / 15 years
= $4,320 annual payment
If interest rate reduce = 4.5%
= $60,000 * 4.5% = $2,700
= $62,700 / 15 years
= $4,180
Step-3:
House cost = $400,000
Down payment = $100,000
Remaining payment = $300,000 * 4.5% interest
= $13,500
= $313,500 / 30 years
= $10,450 for year /12
= $871 for month
His salary should be = $3,111 for month
Step-4:
For children’s needed money = $200,000
Time period = 10years
Each year needed to put away = $20,000 annually
$1,667 for monthly