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a. What is the duration of the loan under both methods of payment? Two-year loan: Interest at end of year one; Principal and interest at end of year two Par value = $100,000 Annual payments = 10% R = 10% Maturity = 2 years PV of CF X PV of CF $10,000 $9,090.91 $9,090.91 $110,000 $90,909.09 $181.818.18 $100,000.00 $190,909.09 Duration = $190,909.09/$100,000 = 1.9091 Two-year loan: Amortized over two years Par value = $100,000 Coupon rate = 10% Annual amortized payments R= 10% Maturity = 2 years = $57,619.05 PV of CFX CF PV of CF 1 $57,619.05 $52,380.95 $52,380.95 2 $57,619.05 $47,619.05 $95,238.10 $100,000.00 Duration = $147,619.05/$100,000 = 1.4762 $147,619.05 Explain the difference in the two results? b. Duration decreases dramatically when a portion of the principal is repaid at the end of year one. Duration often is described as the weighted-average maturity of an asset. If more weight is given to early payments, the effective maturity of the asset is reduced. a. What is the duration of the loan under both methods of payment? Two-year loan: Interest at end of year one; Principal and interest at end of year two Par value = $100,000 Annual payments = 10% R = 10% Maturity = 2 years PV of CF X PV of CF $10,000 $9,090.91 $9,090.91 $110,000 $90,909.09 $181.818.18 $100,000.00 $190,909.09 Duration = $190,909.09/$100,000 = 1.9091 Two-year loan: Amortized over two years Par value = $100,000 Coupon rate = 10% Annual amortized payments R= 10% Maturity = 2 years = $57,619.05 PV of CFX CF PV of CF 1 $57,619.05 $52,380.95 $52,380.95 2 $57,619.05 $47,619.05 $95,238.10 $100,000.00 Duration = $147,619.05/$100,000 = 1.4762 $147,619.05 Explain the difference in the two results? b. Duration decreases dramatically when a portion of the principal is repaid at the end of year one. Duration often is described as the weighted-average maturity of an asset. If more weight is given to early payments, the effective maturity of the asset is reduced