Question

2. 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)_{ar{n|}}] + v^{n+1} frac{n}{i} = v left[ frac{ddot{a}_{ar{n|}} - nv^n}{i} ight] + v^{n+1} frac{n}{i} = frac{vddot{a}_{ar{n|}}}{i} = frac{a_{ar{n|}}}{i} = frac{a_{ar{n|}.105}}{.105} = 77.1, a_{ar{n|}.105} = 8.0955 frac{1 - v^n}{i} = 8.0955, 1 - v^n = 0.105 cdot 8.0955 = 0.8500275, v^n = 0.1499725, -n cdot ln 1.105 = ln 0.1499725, n = -frac{ln 0.1499725}{ln 1.105} = 19.002 Alternatively: PV = -8.0955, I/Y = 10.5, PMT = 1, CPT N = 19 Answer: C.

          2. 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)_{ar{n|}}] + v^{n+1} frac{n}{i} = v left[ frac{ddot{a}_{ar{n|}} - nv^n}{i} 
ight] + v^{n+1} frac{n}{i} = frac{vddot{a}_{ar{n|}}}{i} = frac{a_{ar{n|}}}{i} = frac{a_{ar{n|}.105}}{.105} = 77.1, a_{ar{n|}.105} = 8.0955

frac{1 - v^n}{i} = 8.0955, 1 - v^n = 0.105 cdot 8.0955 = 0.8500275, v^n = 0.1499725, -n cdot ln 1.105 = ln 0.1499725,
n = -frac{ln 0.1499725}{ln 1.105} = 19.002

Alternatively: PV = -8.0955, I/Y = 10.5, PMT = 1, CPT N = 19 Answer: C.

$2. A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, ..., n at the end of year (n+1). After year (n+1), the payments remain constant at n. the annual effective interest rate is 10.5%. Calculate n. (A) 17 (B) 18 (C) 19 (D) 20 (E) 21 PV = v[(Ia)arn|] + v^n+1 fracni = v left[ fracddotaarn| - nv^ni ight] + v^n+1 fracni = fracvddotaarn|i = fracaarn|i = fracaarn|.105.105 = 77.1, aarn|.105 = 8.0955 frac1 - v^ni = 8.0955, 1 - v^n = 0.105 cdot 8.0955 = 0.8500275, v^n = 0.1499725, -n cdot ln 1.105 = ln 0.1499725, n = -fracln 0.1499725ln 1.105 = 19.002 Alternatively: PV = -8.0955, I/Y = 10.5, PMT = 1, CPT N = 19 Answer: C.$

Added by Janet R.

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