Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Matematika Keuangan |
Periode Ujian |
: |
November 2019 |
Nomor Soal |
: |
25 |
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 |
- Case 1, Nilai kini dari pembayaran 2 dan 4 pada tahun-n dan 2n ialah sebesar 2
- Case 2, Nilai kini dari pembayaran 2,4,8, pada tahun-n, 2n, dan 3n.
|
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 |
I truly appreciate your technique of writing a blog. I added it to my bookmark site list and will
Wow, awesome weblog layout! How long have you ever been blogging for?
you made blogging glance easy. The full look of your site is great,
let alone the content material! https://Xdpascal.com/index.php/User:ElizaWorsham54
Good post. I learn something new and challenging on sites I stumbleupon everyday.
It’s always helpful to read through content from other authors and use something from their web sites.
I’m not sure exactly why but this web site is loading very slow
for me. Is anyone else having this problem or is it a issue on my end?
I’ll check back later and see if the problem still exists.
Thank you for another excellent post. Where else may anyone get
that type of information in such an ideal method
of writing? I’ve a presentation subsequent week, and I’m on the search for such information.
Great information. Lucky me I found your site by accident (stumbleupon).
I have book-marked it for later! http://saju.codeway.kr/index.php/User:ArleneMajor9
Do you mind if I quote a couple of your articles as long as I provide credit and sources back to
your webpage? My website is in the very same area of interest as yours and my
visitors would really benefit from some of the information you provide here.
Please let me know if this okay with you. Regards! https://www.vander-Horst.nl/wiki/User:GregSylvia05011
It’s going to be ending of mine day, but before ending I am reading this impressive piece of writing to improve my knowledge.
Heya! I just wanted to ask if you ever have any issues with hackers?
My last blog (wordpress) was hacked and I ended up losing many
months of hard work due to no backup. Do you have any methods to protect against hackers? https://Listingpanda.ca/author/lydia19l984/
Heya i’m for the primary time here. I came across this board
and I to find It truly useful & it helped me out a lot.
I hope to provide something again and help others like you helped me. https://Www.vander-Horst.nl/wiki/User:RodrickCornelius
Hi! Would you mind if I share your blog with my twitter group?
There’s a lot of people that I think would really appreciate your content.
Please let me know. Thanks https://Rowan.wiki/index.php/Outils_Urbain
Unquestionably believe that which you stated. Your
favorite justification seemed to be on the net the simplest thing to be aware of.
I say to you, I definitely get irked while people
think about worries that they plainly do not know about. You managed to hit the nail upon the top and defined out the whole thing without having side-effects , people can take a signal.
Will likely be back to get more. Thanks
I know this web page offers quality dependent articles and extra
data, is there any other web site which gives these kinds of information in quality?
I think everything posted was very logical. However, think on this,
what if you composed a catchier title? I mean,
I don’t wish to tell you how to run your website, however suppose you
added a headline that makes people want more? I mean Pembahasan Ujian PAI:
A10 – No. 25 – November 2019 – Data Polis is a little plain. You
should glance at Yahoo’s home page and see how they create post headlines to get viewers to click.
You might add a video or a related picture or two to grab readers excited about everything’ve got to say.
Just my opinion, it would bring your website a little
bit more interesting.
I like the helpful information you provide in your articles.
I’ll bookmark your blog and check again here regularly.
I am quite sure I’ll learn many new stuff right here!
Good luck for the next!
Thank you for some other great post. The place else
could anybody get that kind of info in such an ideal manner of
writing? I have a presentation next week, and I am at the look for such information.
you are in reality a just right webmaster.
The website loading pace is amazing. It sort of feels that you’re doing
any unique trick. Moreover, The contents are masterwork.
you’ve performed a great task in this topic!
Its like you read my mind! You appear to know a lot about this, like you wrote the book in it or something.
I think that you could do with some pics to drive the message home
a bit, but instead of that, this is great blog.
A fantastic read. I’ll definitely be back. https://checkbookmarks.com/story1242671/cim-investigaci%C3%B3n