Question

You are trying to decide a present worth of a contract. You will receive $10,000 when the contract is signed, a $20,000 payment at the end of Year 1, and $30,000 at the end of Year 2. and $40,000 at the end of Year 3, and $50,000 at the end of Year 4 when the project is completed. Your annual costs for this project are $10,000 per year. What is the present worth of the contract at 5%? Must use gradient method A building is priced at $105,000. If a down payment of $15,000 is made and payments of $3,005 every 3 months thereafter are required, how many years will be necessary to pay for the building? Interest is charged at 4% compounded quarterly You are considering buying a 20-year bond that was issued 2 years ago. Its coupon rate is 4% and interest rates are made semiannually. Its face value is $1000. If the current market interest rate is 6.09%, what should be the bond's price? A woman is planning to retire in 10 years. She wishes to deposit a regular amount every six months until she retires, so that beginning one year following retirement she will receive annual payments of $20,000 for the next 20 years. How much must be deposited every six months if the annual nominal interest rate is 8%, compounded semiannually? Your company predicts your product's sales volume (s) depends on its units selling price (P) as $ $250-P The production cost ic) is $1500 +45 1. Determine the breakeven point, lowest sales volume at which totals sales income just equals total production costs: 2. Determine the sales volume (s) at which your company profit is maximum You are receiving 3 bids for a small project that will take 1 year to complete. Your MARR is 12% nominal interest rate, compounded monthly Show which company should be awarded the job? Company A quotes the job at $50,000 with a payment schedule of 50% payable immediately, 20% payable in 6 months, and 30% payable at the year end. 2. Company B quotes the job at $47,000 with a payment due immediately Company Cquotes the job at $48,000 with 25% payable immediately, and 50% in 6 months, and 25% payable at year end
only numbers 2,3, and 6

Answer 1

2.

Quarterly rate = 4%/4 = 1%

Let, number of quarters required = n

Then,

105000 = 15000 + 3005*(1-1/(1+1%)^n)/1%

Or,

(1-1/1.01^n) = 1%*((105000-15000)/3005)

(1-1/1.01^n) = .2995

1/1.01^n = 1-.2995

1/(1-.2995) = 1.01^n

1.01^n = 1.42755

n = log(1.42755)/log (1.01)

n = 35.78 quarters

So, number of years required = 8.95 years or 9 years

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3.

Number of semiannual payments left = 36 semiannual payment (18 years)

Semiannual coupon payment = (4%/2)*1000 = $20

Semiannual interest rate = 6.09%/2 = 3.045%

So,

Price of the bond = 20*(1-1/(1+3.045%)^36)/3.045% + 1000/1.03045^36

Price of the bond = $773.38 or $773

So, price of the bond should be $773.38 or $773.

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