Revision as of 23:58, 26 November 2023 by Admin (Created page with "Determine the sinking fund deposit by using a 30-year annuity-due accumulation factor (the sinking fund must accumulate to $500,000 after 30 years). The 10 th deposit will be made at time 9 , so you want the sinking fund balance at time 9. Use the sinking fund deposit and a 9 -year annuity-due accumulation factor to determine the balance. <math display="block"> 500000=D \ddot{s}_{\overline{30} \mid .1} \text { so } D=500000 / \ddot{s}_{\overline{30} \mid}=500000 / 180.9...")
Exercise
ABy Admin
Nov 26'23
Answer
Determine the sinking fund deposit by using a 30-year annuity-due accumulation factor (the sinking fund must accumulate to $500,000 after 30 years). The 10 th deposit will be made at time 9 , so you want the sinking fund balance at time 9. Use the sinking fund deposit and a 9 -year annuity-due accumulation factor to determine the balance.
[[math]]
500000=D \ddot{s}_{\overline{30} \mid .1} \text { so } D=500000 / \ddot{s}_{\overline{30} \mid}=500000 / 180.943425=2763.29466
[[/math]]
The amount immediately prior to the tenth deposit will be the accumulated amount including the tenth deposit less the tenth deposit. i.e.
[[math]]
D s_{\overline{10} \mid i=.10}-D=D\left(s_{\overline{10} \mid i=.10}-1\right)=2763.29466(15.93742-1)=41276.51
[[/math]]
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.