4 0/3 points • Perpetuity #1 makes annual payments and has a present value of $50. The first payment is $1 at the end of the first period and each payment thereafter increases by \(k\)%. • Perpetuity #2 makes annual payments and has a present value of $40. The first payment is $1 at the end of the first period and each payment thereafter decreases by \(k\)%. • Each perpetuity operates under the same annual effective interest rate \(i\)%. Find \(i\). 2.00% 2.25% 2.50% 2.75% 3.00%
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We are given that $PV_1 = 50$ and $PV_2 = 40$. The first payment for both perpetuities is $1. The payments for perpetuity #1 increase by $k\%$ each year, and the payments for perpetuity #2 decrease by $k\%$ each year. The present value of a growing perpetuity is Show more…
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5) An annuity in perpetuity with effective annual interest rate i > 0 has present value $1, 000. Find i if the annuity pays $52.50 at the end of every 6 month period, with the first payment at the end of the first year.
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A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, ..., n at the end of year (n+1). After year (n+1), the payments remain constant at n. the annual effective interest rate is 10.5%. Calculate n. (A) 17 (B) 18 (C) 19 (D) 20 (E) 21 PV = v[(Ia)_{n|}] + v^{n+1} * n/i = v[ (ä_{n|} - nv^n) / i ] + v^{n+1} * n/i = (v ä_{n|}) / i = a_{n|} / i = (a_{n|.105}) / .105 = 77.1, a_{n|.105} = 8.0955 (1 - v^n) / i = 8.0955, 1 - v^n = 0.105 * 8.0955 = 0.8500275, v^n = 0.1499725, -n * ln 1.105 = ln 0.1499725, n = - (ln 0.1499725) / (ln 1.105) = 19.002 Alternatively: PV = -8.0955, I/Y = 10.5, PMT = 1, CPT N = 19 Answer: C.
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