Pembahasan Ujian PAI: A10 – No. 15 – Juni 2015

• Perpetuitas Doni: \(3250 = 130{a_{\left. {\overline {\, \infty \,}}\! \right| }}\)
• Anuitas Dina: n = 20
• naik sebesar 15 setiap tahun

• \({{\ddot a}_{\left. {\overline {\,n \,}}\! \right| }} = \frac{{1 – {v^n}}}{d}\)
• \({a_{\left. {\overline {\, \infty \,}}\! \right| }} = \frac{1}{i}\)

Prepetuitas Dina:
\(3250 = P{{\ddot a}_{\left. {\overline {\, {20} \,}}\! \right| }} + 15\left( {\frac{{{a_{\left. {\overline {\, {19} \,}}\! \right| }} – 19{v^{19}}}}{i}} \right)\) \({{\ddot a}_{\left. {\overline {\, {20} \,}}\! \right| }} = \frac{{1 – {v^{20}}}}{d} = \frac{{1 – {{(1,0417)}^{ – 20}}}}{{\frac{{0,0417}}{{1,0417}}}} = 13,9462984\) \({{\ddot a}_{\left. {\overline {\, {19} \,}}\! \right| }} = \frac{{1 – {v^{19}}}}{d} = \frac{{1 – {{(1,0417)}^{ – 19}}}}{{\frac{{0,0417}}{{1,0417}}}} = 13,486159\) \(3250 = P\left( {13,9462984} \right) + 15\left( {\frac{{\left( {13,486159} \right) – 19{{\left( {1,0417} \right)}^{ – 19}}}}{{0,0417}}} \right)\) \(3250 = P\left( {13,9462984} \right) + 1706,299\) \(P = 110,6889\)