In option 1 the payments occur at the beginning of

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the present value of each option and compare them. In Option 1, the payments occur at the beginning of each period, so it is an annuity due . The timeline for the ten cash flows is: 0 1 2 9 10 25,000 25,000 25,000 25,000 Recall that the value of an annuity due is the value of an otherwise similar ordinary annuity * (1+r). Thus, the expression to solve for the value of this annuity due would be as follows: APV due = $25,000 * 06 . 1 * 06 . ) 06 . 1 ( 1 1 10 - = $195,042.31 You can also solve this problem by setting your calculator's TVM settings to begin mode and directly inputting the information into the calculator as follows. Just remember to change the setting back to end mode when you are done. N I PV PMT FV 10 6 CPT 25,00 0 -195,042.31 The second option is to receive $190,000 today (this is already at PV) Solution : Choose Option 1. $195,042.31 > $190,000 b. If the two choices are to be equivalent, then the present value of the ten payments must equal $190,000. The setup would be as follows: $190,000 = $25,000 * ) 1 ( * ] ) 1 ( 1 1 [ 10 r r r + + - Solve for r on your financial calculator as follows: Set your calculator to Begin mode, then: N I PV PMT FV 10 CPT -190,000 25,00 0 6.697 Solution : The rate at which the two choices have equal present values is 6.697%. F301 TVM practice set I solutions 3
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6. The first thing you should note is that there is a mismatch of periods . The payments are given in years , but the compounding period is given in months . To solve the problem, the periods must match. So if you use the monthly rate of 0.75% per month, then the number of periods is 24 for the first payment and 84 for the second. Alternatively, you can use years as the periods and convert the discount rate to an effective annual rate by compounding the monthly rate for a year: [ ] [ ] ...% 3806 . 9 1 ) 0075 . 1 ( 1 ) 1 ( 12 = - = - + = = year per months rate monthly EAR year per Rate The annual timeline looks like this: 0 1 2 3
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