Class 7 Jan 25th Completed

Old example present value of an annuity m recall the

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Old Example: Present Value of an Annuity M Recall the example from before: Interest rate is 10% per year. M Timeline: 0 1 2 3 4 Periods -----|----------|----------|----------|----------|--------------- PV = ? 1,000 1,000 1,000 1,000 Cash Flows 87 . 169 , 3 $ 1 . 0 ) 1 . 1 ( 1 000 , 1 $ ) 1 ( 1 0 4 0 0 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = PV PV r r A PV n 9
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10 Car Buying Example M You start a new job and think you have enough money to pay $500 per month for a new car. Suppose the car dealerships right now offer to lend money at 12% per year compounded monthly for 48 months with a zero downpayment. How much can you spend on a car today? Assume the first payment is due exactly one month after you buy the car. Timeline: 0 1 2 3 4 ……… . 46 47 48 ----|------|------|------|------|-------------------------|------|------|------ 500 500 500 500 ………… .. 500 500 500 ( ) 98 . 986 , 18 $ 01 . 0 01 . 1 1 500 01 . 1 500 ........ 01 . 1 500 01 . 1 500 01 . 1 500 48 48 3 2 0 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = + + + + = PV
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iClicker Example: PV of an Annuity Due (1) M Recall the example from before, but assume your grandparents plan to give your sister $1,000 at the beginning of each year in college (starting now) for four years. What is the present value of this annuity? As before, the interest rate is 10% per year. An annuity where payments are made at the beginning of each period is called an annuity due. Draw a timeline! M a) $3,169.87 b) $2,486.85 c) $2,881.70 d) $3,486.85 e) None of the above. 11
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iClicker Example: PV of an Annuity Due (2) M Recall the example from before, but assume your grandparents give your sister $1,000 at the beginning of each year in college (starting now) for four years. What is the present value of this annuity? As before, the interest rate is 10% per year.
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