Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Pembayaran sebesar 2 dan 4 masing-masing pada n tahun dan 2n tahun dari sekarang memiliki nilai kini sebesar 2 pada suatu tingkat bunga i>0. Tentukan nilai kini dari pembayaran sebesar 2, 4, dan 8 masing-masing pada n tahun, 2n tahun, dan 3n tahun dari sekarang.
a. 2,5
b. 3
c. 4
d. 4,5
e. 6
| Diketahui |
|
| Rumus yang digunakan | Present Value Factor, \(v = \frac{1}{{{{\left( {1 + i} \right)}^t}}} = {\left( {1 + i} \right)^{ – t}}\) |
| Proses pengerjaan | Case 1
\(A\left( 0 \right) = 2 = 2{\left( {1 + i} \right)^{ – n}} + 4{\left( {1 + i} \right)^{ – 2n}}\) asumsikan \({\left( {1 + i} \right)^{ – n}} = X\)
\(A\left( 0 \right) = 2 = 2X + 4{X^2}\)
dengan formula \(\frac{{ – b \pm \sqrt {{b^2} – 4.a.c} }}{{2.a}}\) didapati: \(X = 0,5\;;X = \; – 1\) Case 2 \(A\left( 0 \right) = 2{\left( {1 + i} \right)^{ – n}} + 4{\left( {1 + i} \right)^{ – 2n}} + 8{\left( {1 + i} \right)^{ – 3n}}\) \(A\left( 0 \right) = 2 + 8{X^3}\;\), dimana \(X = {\left( {1 + i} \right)^{ – n}} = 0,5\) \(A\left( 0 \right) = 2 + 8{\left( {0,5} \right)^3}\) \(A\left( 0 \right) = 2 + 1\) \(A\left( 0 \right) = 3\) |
| Jawaban | b. e |
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