Revision as of 00:08, 19 November 2023 by Admin (Created page with "'''Solution: C''' The accumulated value is <math display = "block">1000 \ddot{s}_{\overline{20}|0.0816}=50,382.16.</math> This must provide a semi-annual annuity-due of 3000. Let n be the number of payments. Then solve <math display = "block">3000 \ddot a_{\overline{n}|0.04} = 50,382.16</math> for <math>n = 26.47</math>. Therefore, there will be 26 full payments plus one final, smaller, payment. The equation is <math display = "block">50,382.16 = 3000 \ddot a_{\over...")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: C
The accumulated value is
[[math]]1000 \ddot{s}_{\overline{20}|0.0816}=50,382.16.[[/math]]
This must provide a semi-annual annuity-due of 3000. Let n be the number of payments. Then solve
[[math]]3000 \ddot a_{\overline{n}|0.04} = 50,382.16[[/math]]
for [math]n = 26.47[/math]. Therefore, there will be 26 full payments plus one final, smaller, payment. The equation is
[[math]]50,382.16 = 3000 \ddot a_{\overline{n}|0.04} + X (1.04)^{-26}[[/math]]
with solution [math]X = 1430[/math]. Note that the while the final payment is the 27th payment, because this is an annuity-due, it takes place 26 periods after the annuity begins.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.