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Unformatted text preview: an Amortization Borrow $1,000 today, how much would the annual Borrow payments be if you are required to repay in two years and the interest rate is 10%? years PVA = PMT( 1 1,000 = PMT(.1 1,000 1 i 1 i(1+i)n ) 1 .1(1+.1)2 ) –576.19 1,000 = PMT(1.736) 1,000 PMT = 576.19 N 2 I/YR PV PMT FV 10 1,000 ? 13 Present Value of an Annuity Loan Amortization Borrow $1,000 today, how much would the annual Borrow payments be if you are required to repay in two years and the interest rate is 10%? years 0 1 $1,000 +$100 2 $1,100 -$576.19 $523.81 $576.19 +$52.38 -$576.19 $0.00 14 Present Value of an Annuity Example #1 Bob borrows $5,000 from his parents to purchase a Bob used car. He agrees to make payments at the end of each year for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? this 0 1 2 3 4 $5,000 $? $? $? $? 5,000 = 5,000 5 1 1 PMT(.06 .06(1+.06)5) $? –1,186.98 5,000 = PMT(4.2124) 5,000 PMT = $1,186.98 N 5 I/YR PV PMT FV 6 5,000 ? 15 Present Value of an Annuity Example #1a Bob borrows $5,000 from his parents to purchase a Bob used car. He agrees to make payments at the end of each month for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? payments? 0 1 $5,000 5 1 5,000 = PMT( 1 ) 5,000 60 .005 .005(1+.005) 5,000 = PMT(0.0193) 5,000 PMT = $96.66 Cannot divide the annual payment Cannot divide the annual payment by 12 to get monthly payment. Why? by 12 to get monthly payment. Why? –96.66 N I/YR PV PMT FV 60 0.5 5,000 ? 16 Future Value of an Annuity Two Types of Annuities Ordinary Annuity - Payments (or deposits) occur at Ordinary the end of the period end 0 $0 1 $100 2 FV = $205 $100 Annuity Due - Payments (or deposits) occur at the Annuity beginning of the period beginning 0 1 2 $100 $100 FV = ? Each payment (or deposit) for an annuity due earns one Each additional period interest. additional 17 Interest Rates:Effective Annual Rate (EAR) This is the actual rate paid (or received) This after account...
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