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林君達 H34945018 工程經濟 6/24/2017 4.7 As a typical middle-class consumer, you are making monthly payments on your home mortgage (9% annual interest rate), car loan (12%), home improvement loan (14%), and past-due charge accounts (18%). Immediately after getting a $100 monthly raise, your friendly mutual fund broker tries to sell you some investment fund with a guaranteed return of 10% per year. Assuming that your only other investment alternative is a savings account, should you buy? Yes. 4.27 Suppose a young newlywed couple is planning to buy a home two years from now. To save the down payment required at the time of purchasing a home worth $220,000 (let's assume that the down payment is 10% of the sales price, or 22,000), the couple decides to set aside some money from each of their salaries at the end of every month. If each of them can earn 6% interest (compounded monthly) on his or her savings, determine the equal amount this couple must deposit each month until the point is reached where the couple can buy the home. 6% Compounded Monthly = 0.5% Monthly N = 24 months Target = $22,000 A = $22,000 (A/F, 0.5%, 24) = $828.34 4.37 Sam Salvetti is planning to retire in 15 years. Money can be deposited at 8% compounded quarterly. What quarterly deposit must be made at the end of each quarter until Sam retires so that he can make a withdrawal of $25,000 semiannually over the first five years of his retirement? Assume that his first withdrawal occurs at the end of six months after his retirement. 8% Compounded Quarterly = 2% Interest per quarter $25,000 semiannually over five years = $25,000 x 10 = $250,000 = F Amount needed at the end of 15 years = $149,829.81 N = 15 years x 4 = 60 A = $149,829.81 (A/F, 2%, 60) = $1,276.97 -1- 林君達 H34945018 工程經濟 6/24/2017 4.47 An automobile loan of $20,000 at a nominal rate of 9% compounded monthly for 48 months requires equal end-of-month payments of $497.70. Complete the following table for the first six payments, as you would expect a bank to calculate the values: 9% Compounded monthly = 0.75% month End Of Interest Month Payment Repayment Remaining Loan of Principle Balance 1 $150.00 $347.70 $19,652.30 2 $147.39 $350.31 $19,301.99 3 $144.76 $352.94 $18,949.06 4 $142.12 $355.58 $18,593.48 5 $139.45 $358.25 $18,235.23 6 $136.76 $360.94 $17,874.29 4.57 To buy a $150,000 house, you take out a 9% (APR) mortgage for $120,000. Five years later, you sell the house for $185,000 (after all other selling expenses). What equity (the amount that you can keep before tax) would you realize with a 30-year repayment term? Total Amount = $150,000 Initial Loan = $120,000 APR = 9% N = 360 Yearly Payment = PMT(9%,30,-120000) = $11,680.36 Remaining Loan on 5th year = $114,731.29 $185,000-$115,056.16-$30,000 = $5,268.71 -2-