# Busn380 - Week 1 Problem Set 1

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Week 1: Problem Set 1 1. Ben Collins plans to buy a house for \$65,000. If that real estate property is expected to increase in value 5 percent each year, what would its approximate value be seven years from now? Answer: PV * FVF or, PV (1 + .05)^n or, PV (1.05)^7 or, PV * 1.4071 or, \$65,000 * 1.4071 = \$91,461.50 2. At an annual interest rate of five percent, how long would it take for your savings to double? Answer: Future Value Factor = (1 + i)^n or, FVF = (1 + .05)^14.21 or, FVF = 2.000322: Where \$1,000 * 2.000322 = \$2,000.3221 or, rounded to the nearest whole dollar it would take 14.21 years with a 5% APR to double one’s savings. 3. In the mid-1990s, selected automobiles had an average cost of \$12,000. The average cost of those same motor vehicles is now \$20,000. What was the rate of increase for this item between the two time periods? Answer: Using an increment of 15 years; PV * FVF or, PV (1 + i)^n or, PV (1.0347)^15 or, \$12,000 * 1.6681 = \$20,017.20; Alternatively, PV (1.0346)^15 or, \$12,000 * 1.6657 = \$19,988.40; So, we can see the rate of increase was between 3.46% and 3.47% each year for 15 years. 4. A family spends \$28,000 a year for living expenses. If prices increase by 4 percent a year for the next three years, what amount will the family need for its living expenses? Answer: PV (1 + i)^n or, PV (1 + .04)^3 or, \$28,000 * 1.125 = \$31,500 needed for the family’s annual living expenses. 5. What would be the yearly earnings for a person with \$6,000 in savings at an annual interest rate of 5.5 percent? Answer: PV (1 + i)^n - PV or, \$6,000 * 1.055 - \$6,000 = \$330 in yearly earnings. 6. Elaine Romberg prepares her own income tax return each year. A tax preparer would charge her \$60 for this service. Over a period of 10 years, how much does Elaine gain from preparing her own tax return? Assumes she can earn 3 percent on her savings.