A 30-year $500,000 loan is paid off via the accumulation of a sinking fund. Sinking fund deposits are made at the beginning of each year. If the effective annual interest rate earned on the sinking fund is 10%, determine the amount in the sinking fund immediately prior to the 10th deposit.

• 37,800
• 38,700
• 39,400
• 40,300
• 41,300

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

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.