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CHAPTER 6 B-73 14. For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m )] m – 1 So, for each bank, the EAR is: First National: EAR = [1 + (.1420 / 12)] 12 – 1 = .1516 or 15.16% First United: EAR = [1 + (.1450 / 2)] 2 – 1 = .1503 or 15.03% Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR. 15. The reported rate is the APR, so we need to convert the EAR to an APR as follows: EAR = [1 + (APR / m )] m – 1 APR = m [(1 + EAR) 1/ m – 1] APR = 365[(1.16) 1/365 – 1] = .1485 or 14.85% This is deceptive because the borrower is actually paying annualized interest of 16% per year, not the 14.85% reported on the loan contract. 16. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = \$2,100[1 + (.084/2)] 34 = \$8,505.93 17. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t It is important to note that compounding occurs daily. To account for this, we will divide the interest rate by 365 (the number of days in a year, ignoring leap year), and multiply the number of periods by 365. Doing so, we get: FV in 5 years = \$4,500[1 + (.093/365)] 5(365) = \$7,163.64 FV in 10 years = \$4,500[1 + (.093/365)] 10(365) = \$11,403.94 FV in 20 years = \$4,500[1 + (.093/365)] 20(365) = \$28,899.97

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