密西根大学罗斯商学院 金融导论公开课 作业2 解答

Question 1

(5 points) Qin deposits his first paycheck in the bank. The annual interest rate is 12%, but interest is compounded quarterly. The EAR is: ·12.55 ；(1+12%/4）^4-1=12.55%

Question 2

(5 points) Ranjit began setting aside $6,000 per year in a mutual fund at the age of 25. He has turned 34, and has just made a deposit. The mutual fund has returned 6.5% annually. How much does Rajit have in his account today?

·80967 ； =FV(0.065,10,6000)

Question 3

(5 points) Mohammad has just turned 21 and now has access to the money his parents have been putting away in an account for him since he was 5 years old. His mother has asked him to guess what his account is worth given that they have invested $1,000 every year in the account starting on his 5th birthday and have just made one. The interest rate on the account has been 3.5% annually. How much is Mohammad’s account worth today? (Enter just the number without the $ sign or a comma; round off decimals.)

·22705 ； =FV(0.035,17,1000) 注意 n=17，想一下第一年年底也就是刚满六岁时的2035

Question 4

(5 points) Marcel has just graduated from college and has found a job that will pay him $25,000 per year at the end of each year, but the job is only for 5 years. He is not worried about that because he plans to do an MBA after gaining 5 years experience anyway. What is the value today of his 5-year salary assuming that the interest rate is 3%?

·114493 ；=PV(0.03,5,25000) Question Explanation

Mechanics of the calculation of the PV of an annuity. The maximum value of his entire 5-year salary is $125,000. Why?

Question 5

(10 points) Hueling owns a rental property on Main street, but she is considering selling the property to another real estate investor. In preparation for negotiating a price, Hueling wants to know the value of the property.The Net Operating Income (NOI) is the cash flow from real estate and the Cap Rate is the rate, where NOI is rental revenue less all expenses except loan servicing. The property has an NOI of $12,000 per year. The local real estate market has a cap rate of 6%. What is a fair price for the property assuming that the building's life is 35 years?(Enter just the number without the $ sign or a comma; round off decimals.) ·173979 ； =PV(0.06,35,12000)

Question 6

(10 points) Roxanne is in the market for a new house, and she has found a house she likes that is selling for $250,000. The down payment on the house is 20% (the amount that the bank should require you to pay in cash) and Roxanne plans to finance the remainder with a fixed rate

mortgage. The annual rate is 6% and the mortgage is for 15 years, though payments are monthly. What is the interest component of Roxanne's first monthly payment? ·1000

Question Explanation

This is a simple question, but one which shows your understanding of a loan and what the interest is a function of.

1. PMT on 200.000 is 1,687.71, so this is:

=PMT(0.06/12,180,200000) This is your PMT which includes the repayment of the loan AND interest

2. After the very first payment (in the first period), the remaining loan balance for period 179-or PV-is

=PV(0.06/12,179,1687.71)

3. 200.000-$199,311.85=688.15 This is a total repayment of the loan, NOT including percentage. so...

4. 1687.71-688.15 (just the repayment without percentage)=your percentage

Question 7

(15 points) Baako has invested $75,000 in a trust fund at 9% for his child's college education. His child will draw $30,000 per year for four years, starting at the end of year 7. What will be the amount that will be left over in the education fund at the end of year 10 (just after the child has withdrawn the fourth time)?(Enter just the number without the $ sign or a comma; round off decimals.)

·40358；

A multi-layer problem, now that you know how to calculate basic stuff. Draw a timeline; it is key. Remember a spreadsheet is a time line.

End of year : 7 : 75,000*(1+9%)^7 – 30,000 =107102.9341 8: 107102.9341 – 30,000 = 86742.19813

9: 过程同上得64548.99596 10:40358.40559

Question 8

(15 points) Two years ago Abilia purchased a $10,000 car; she paid $2000 down and borrowed the rest. She took a fixed rate 60-month installment loan at a stated rate of 8% per year. Interest rates have fallen during the last two years and she can refinance her car by borrowing the amount she still owes on the car at a new fixed rate of 6% per year for 3 years. Should Abilia refinance her loan? How much will she save per month for the next three years if she decides to refinance? ·yes ,5;

Question Explanation

This again is a multi-layer question. Understanding the problem first is the key, and using time lines is the main way you will. Loan=8000,

Monthly payment as PMT1: =PMT(.08/12,60,8000) = 162.21 Rest of loan as PV1 : =pv(.08/12,36,162,21) = 5176.41

New payment as PMT2: =pmt(.06/12,36,5176.41) = 157.48 Saving Per Month :PMT1 – PMT2 = 4.73

Question 9

(15 points) Two years ago, you purchased a $20,000 car, putting $4,000 down and borrowing the rest. Your loan was a 48-month fixed rate loan at a stated rate of 6% per year.You paid a non-refundable application fee of $100 at that time in cash. Interest rates have fallen during the last two years and a new bank now offers to refinance your car by lending you the balance due at a stated rate of 4% per year. You will use the proceeds of this loan to pay off the old loan. Suppose the new loan requires a $200 non-refundable application fee. Given all this information, should you refinance? How much do you gain/lose if you do? ·NO, lose 25

Question Explanation

This is an even more realistic version of the mortgage problem. Think carefully about time lines and relevant interest rates to make different calculations Loan =16000

1. payment1 pmt1: =pmt(.06/12,48,16000) = 375.76 2.rest loan pv1: =PV(0.06/12,24,375.76) = 8478.22

3.payment2 pmt2: =PMT(0.04/12,24,8478.22) = 368.17 4` pmt1 – pmt2 = 7.59

5` PV of the saving : =pv(.04/12,24,7.59) = 174.78 6` 174.78 – 200 = - 25.22

Question 10

(15 points) You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,500 cash rebate from Dealer A. The price of the car is $15,000. (ii) Lease the car from Dealer B. Under this option, you pay the dealer $500 now and $200 a month for each of the next 36 months (the first $200 payment occurs 1 month from today). After 36 months you may buy the car for $8,000. (iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero interest 36-month loan with monthly payments. The car price is $15,000. Suppose the market interest rate is 6%. What is the net cost today of the cheapest option? (Enter just the number without the $ sign or a comma; round off decimals.Since this asks for a cost, you just enter the number without a negative sign.) ·13500 Optional A:

Net PV = Price – Rebate = 15000-1500 = 13500 Optional B:

Net PV = Initial payment + PV of PMTs + PV of final payment

= 500+pv(.06/12,36,200) + pv(.06/12,36,0,800) = 500 + 6574.20 + 6685.16 = 13759.36

Optional C: Net PV= pv(.06/12,36,15000/36) = 13696.26

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