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CHAPTER 6 B-97 c. Using the cash flows from the loan, we have the PVA and the annuity payments and need to find the interest rate, so: PVA = \$68.92 = \$25[{1 – [1 / (1 + r )] 4 }/ r ] Using a spreadsheet, trial and error, or a financial calculator, we find: r = 16.75% per week APR = 52(16.75%) = 870.99% EAR = 1.1675 52 – 1 = 3141.7472 or 314,174.72% 76. To answer this, we need to diagram the perpetuity cash flows, which are: (Note, the subscripts are only to differentiate when the cash flows begin. The cash flows are all the same amount.) . . C 3 C 2 C 2 C 1 C 1 C 1 Thus, each of the increased cash flows is a perpetuity in itself. So, we can write the cash flows stream as: C 1 /R C 2 /R C 3 /R C 4 /R …. So, we can write the cash flows as the present value of a perpetuity, and a perpetuity of: C 2 /R C 3 /R C 4 /R …. The present value of this perpetuity is: PV = ( C /R) / R = C /R 2 So, the present value equation of a perpetuity that increases by C each period is: PV = C /R + C /R 2

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