ASSIGNMENT
Instructions:
Write out your steps and financial calculator function keys. Complete work is necessary to receive full credit.
1. You want to save some money for your two dream vacations as well as have some money available during your retirement years. Today is your 35th birthday. You want to make annual deposit of $10,000 starting on your 40th birthday, all the way to your 65th birthday. (Please note your last deposit in on your 65th birthday). Your first vacation (to Thailand) will occur on your 50th birthday where you need to withdraw $15,000 for that trip (on your 50th birthday). Similarly, your second vacation (to Australia) will occur on your 60th birthday where you need to withdraw $20,000 for that trip (on your 60th birthday). If your bank pays special interest of 6%, compounded annually on these deposits. How much will be available in your account on your 66th birthday (after you accounted for two withdrawals on your 50th birthday and 60th birthday)?
2. Extension/Modification of Question 1. You want to save some money for your two dream vacations as well as have some money available during your retirement years. Today is your 35th birthday. You want to make semi-annual deposit of $5,000 starting on your 40th birthday, all the way to your 65th birthday. (Please note your last deposit in on your 65th birthday). Your first vacation (to Thailand) will occur on your 50th birthday where you need to withdraw $15,000 for that trip (on your 50th birthday). Similarly, your second vacation (to Australia) will occur on your 60th birthday where you need to withdraw $20,000 for that trip (on your 60th birthday). If your bank pays special interest of 6%, compounded semi-annually on these deposits. How much will be available in your account on your 70th birthday (after you accounted for two withdrawals on your 50th birthday and 60th birthday)?
3. A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at 9% interest versus a 15-year mortgage with 8.5% interest. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan?
4. If 4 years of college are expected to cost $150,000 18 years from now, how much must be deposited now into an account that will average 8% annually in order to save the $150,000? By how much would your answer change if you expected 11% annually?
5. Show numerically that a savings account with a current balance of $1,000 that earns interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000 that carries equal annual payments at 9% interest.
6. Would you prefer a savings account that paid 7% interest, compounded quarterly, over an account that paid 7.5% with annual compounding if you had $1,000 to deposit? Would the answer change if you had $100,000 to deposit?
7. Some home loans involve "points," which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if 0.5 point is charged on a $100,000 loan, the loan repayment schedule is calculated on the $100,000 loan, but the net amount the borrower receives is only $99,500. What is the effective annual interest rate charged on such a loan, assuming that loan repayment occurs over 360 months, and that the interest rate is 1% per month?
Hint: The monthly payment is based on $100,000. Calculate the payment first. The PV that the borrower receives is $99,500. Now think about the nominal rate and then the effective rate.
8. What is the present value of a thirty-year annuity that pays $3000 a year with the annuity first payment occurring in Year 21? (first payment in Year 21) Also, the interest rate is expected to be 4 percent until Year 21 and then to increase to 5 percent hereafter.
9. You are saving for college education of your five children. They are one year apart in age; one will begin college in 10 years (Year 10), another in 11 years, another in 12 years, another in 13 years, and the last one in 14 years. You are planning to at least support them financially (with your personal funds) for the first two years of their college education, and then expect them to get a student loan and or scholarships. You estimate your children's college expenses to be $7,000 per year per child, paid at the beginning of each college year (first payment for first child is at Year 10 and so on). The annual interest rate is 4 percent. How much money must you deposit in an account each year to fund your children's education? You will begin your deposit into the account starting today and the last deposit will be the year before your oldest child enter college.
10. A foreign government has stolen U.S. military's star wars program component and hence the U.S. military is trying to counter that stolen component (technology) with a more sophisticated component. It has asked all the U.S. scientists to come up with one (better component) within 2 years. The U.S. military promised a fixed annual payment of $2 million each for the first ten annual payments (first payment will occur exactly two years from today (Year 2), and the last payment will occur in Year 11) and then they promised to increase that payment by 2% each year annually (starting the eleventh payment. i.e. Year 12) for the next thirty payments. In other words, the eleventh payment (in Year 12) will be $2.04 million and so on. If we assume an interest rate of 4%, what is the present value of this offer to any scientist who takes this challenge? The military also promised that these payments will be federal tax exempted!
11. A baseball player just signed a contact with the Houston Astros. He will receive $3 million upfront (today) and will be receive the subsequent payments as a growing annuity starting next year (one year from today) with a growth rate (g) of 5% for the next 10 years. In other words, the first payment one year from today is 3(1xg) and so on. What is the Present Value of this contract if the interest rate is 6%, compounded annually.
12. Your paycheck today is $80,000 (on your 30th birthday) and you expect your paycheck to increase by 10% each year, starting your 31st birthday all the way to your 60th birthday, when you plan to retire (you will receive your last paycheck on your 60th birthday). Starting today you will set aside 5% of your annual paycheck into a special saving account which pays 14% interest compounded annually. Remember you first deposit into the special account begins today and the last deposit is in your 60th birthday.
a. What is the present value of these deposits into the savings account.
b. Also, what is the future value of these deposits on your 60th birthday?
13. You just turned 21 today. Starting today you plan to invest $500 every six months, first deposit today and last deposit on your 50th birthday. After that, you plan to leave the money in the same account until your turned 65. The interest rate is 3% compounded daily until your last deposit and then it is 4% compounded semi-annually after that. How much money will you have in your account on your 65th birthday?