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ASURANSI JIWA
PENGERTIAN
Asuransi jiwa menyediakan suatu pembayaran santunan asuransi
(claim) dari jumlah yang ditetapkan atas suatu kematian, yang dikenal
sebagai tertanggung (insured).
Dalam pembayaran ini terdapat dua asumsi:
1. pembayaran santunan asuransi pada akhir tahun kematian polis
(asuransi diskrit)
2. pembayaran santunan asuransi pada saat kematian terjadi (asuransi
kontinu).
PRINSIP PRINSIP UMUM ASURANSI JIWA
1. Economic Principles : resiko kematian, resiko hari tua, resiko
kecelakaan/sakit
2. Legal Principle
3. Actuarial Principles
• Dalam asuransi jiwa terdapat hubungan antara hak dan kewajiban yang
dinyatakan dalam besaran besaran : premi, santunan , cadangan premi, nilai
tebus dan lain lain. Hubungan ini ditentukan dengan dasar-dasar perhitungan
• Tingkat bunga (Rate of Interest)
• Tingkat kematian ( Mortality Rate)
• Biaya (Loading Expense )
4. Cooperation Priciples : orang orang yang berkepentingan untuk
menanggulangi kerugian
Jenis asuransi jiwa berdasarkan sistem
pembayaran
1. Asuransi yang dibayarkan seketika pada saat kematian:
a. Asuransi dengan manfaat bertingkat (varying benefit insurance)
b. Asuransi Dwiguna (endowment insurance)
c. Asuransi tertunda (deffered annuities)
d. Asuransi dengan manfaat kematian yang tak tetap
2. Asuransi yang dibayarkan pada akhir tahun kematian:
a. Asuransi jiwa berjangka n-tahun
b. Asuransi jiwa seumur hidup
c. Asuransi jiwa dwiguna
d. Asuransi tertunda
Asistensi - Asuransi Jiwa.pptx
ASURANSI BERJANGKA
Dalam polis asuransi berjangka , uang pertanggungan akan dibayarkan
bila sitertanggung meninggal dalam jangka waktu asuransi.
Misal semua orang yang berusia x tahun (lx) setuju mengumpulkan Rp
A setiap orang dengan perjanjian apabila pada satu tahun berikutnya
ada anggota yang mati maka ahli warisnya akan diberikan Rp 1. Bila
iuran ini dibungakan i/ tahun maka jumlah uang yang terkumpul
adalah:
Asistensi - Asuransi Jiwa.pptx
Asistensi - Asuransi Jiwa.pptx
Seorang (40) mengikuti polis asuransi jiwa dengan santunan manfaat
kematian 10 jt dibayarkan pada akhir tahun kematian dan (i=0.05).
Diberikan fungsi l(x)=100-x; x=0,1,2,….,100
(dengan menggunakan excel dan source code R), hitunglah nilai tunai
Asuransi jiwa berjangka 25 tahun
ILUSTRASI
EXCEL
Hasil R
Axn.diskrit<-function(expr,age,i,B,w,n){
v<-(1+i)^-1
sx<-eval({x=0:w;expr})
output<-NULL
for(k in 1:n){
output[k]<-B*v^(k)*((sx[age+k-1]-sx[age+k])/sx[age+1])}
sum(output)}
expr=expression(100-x)
Axn.diskrit(expr,age=40,i=0.05,B=10000000,w=100,n=25)
[1] 2348991
ASURANSI SEUMUR HIDUP
Dalam polis asuransi seumur hidup, uang pertanggungan akan
dibayarkan bila sitertanggung meninggal sewaktu waktu kematian
terjadi. Ax merupakan nilai tunai (present value) asuransi seumur hidup
dengan santunan Rp 1 bagi orang yang berusia x tahun.
Seorang (40) mengikuti polis asuransi jiwa dengan santunan manfaat
kematian 10 jt dibayarkan pada akir tahun kematian dan (i=0.05).
Diberikan fungsi l(x)=100-x; x=0,1,2,….,100
Hitunglah nilai sekarang Asuransi jiwa seumur hidup
ILUSTRASI
EXCEL
R
Ax.diskrit<-function(expr,age,i,B,w){
v<-(1+i)^-1
sx<-eval({x=0:w;expr})
output<-NULL
for(k in 1:(w-age)){
output[k]<-B*v^(k)*((sx[age+k-1]-sx[age+k])/sx[age+1])}
sum(output)}
expr=expression(100-x)
Ax.diskrit(expr,age=40,i=0.05,B=10000000,w=100)
[1] 3154882
ASURANSI ENDOWMENT
Merupakan gabungan dari asuransi berjangka dan endowment murni.
Dalam polis asuransi dwiguna walaupun sudah habis jangka waktu
asuransi , pemegang polis tetap mendapatkan uang pertanggungan
(santunan).
ASURANSI ENDOWMENT
n
E
x = vn 𝑙𝑥
+
𝑛
𝑙𝑥
Ilustrasi
Seorang (40) mengikuti polis asuransi jiwa dengan santunan manfaat
kematian 10 jt dibayarkan pada akir tahun kematian dan (i=0.05).
Diberikan fungsi l(x)=100-x; x=0,1,2,….,100
Asuransi jiwa dwiguna berjangka (Endowmen) 25 tahun
EXCEL
R
v<-(1+i)^-1
sx<-eval({x=0:w;expr})
output<-NULL
for(k in 1:n){
output[k]<-B*v^(k)*((sx[age+k-1]-sx[age+k])/sx[age+1])}
Exn<-B*v^(n)*(sx[age+n+1]/sx[age+1])
sum(output)+Exn}
expr=expression(100-x)
Endowment.diskrit(expr,age=40,i=0.05,B=10000000,w=100,n=25)
• [1] 4071590
TUGAS INDIVIDU
Seorang (40) mengikuti polis asuransi jiwa dengan santunan manfaat
kematian 10 jt dibayarkan pada akir tahun kematian dan (i=0.05).
Diberikan fungsi survival s(x)=exp(-
0.0001
log(1.09)
(1.09𝑥
-1)) ; x=0,1,2,….,100
Hitunglah nilai sekarang aktuaria untuk (dengan menggunakan excel
dan R):
a. Asuransi jiwa seumur hidup
b. Asuransi jiwa berjangka 25 tahun
c. Asuransi jiwa dwiguna berjangka (Endowmen) 25 tahun

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Asistensi - Asuransi Jiwa.pptx