Lauren takes out a loan of $35,000. She pays this back by establishing a sinking fund and making 16 equal payments at the end of each year. The sinking fund earns 9% each year. Immediately after the 9th payment the sinking fund’s yield increases to 11%. At this time Lauren adjusts her sinking fund payment to X so that the fund will accumulate to $35,000 16 years after the original loan date.

Find X.

• $8,057.17
• $1,291.33
• $647.09
• $1,040.86
• $2,166.06

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Answer C

[math]\mathrm{OB}_0=35,000[/math] 16 years

[math]\mathrm{i}=.09[/math] for 9 years then .11 for 7 years

Initial payments would be:

[[math]] 35,000=\mathrm{xs}_{\overline{16} | .09}=1,060.50 [[/math]]

Just after the [math]9^{\text {th }}[/math] payment the balance would be:

[[math]] 1,060.50 \mathrm{~s}_{\overline{16} |.09}=13,808.81 [[/math]]

At .11 for the next 7 years the accumulated amount will be 35,000 if: :

[[math]] \begin{aligned} & 13,808.81(1.11)^7+\mathrm{xs}_{\overline{7} |0.11}=35,000 \\ & \mathrm{x}=647.09 \end{aligned} [[/math]]

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.