A loan of X is repaid with level payments of R payable at the end of each year for n years. You are given:

i) The interest paid in year 1 is 797.50.

ii) The principal repaid in year n – 4 is 865.

iii) The principal outstanding at the end of year n – 1 is 1144.50.

Determine X

• 9,500
• 10,000
• 10,500
• 11,000
• 11,500

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

[[math]]\begin{aligned} & O B_{n-1}=R a_1=1144.5=R v \\ & P_{n-4}=R v^{n-(n-4)+1}=R v^5=865 \\ & \frac{R v^5}{R v}=v^4=\frac{865}{1144.5}=0.75579 \\ & v^4=0.75579, \quad v=0.93240, \quad i=0.07251 \\ & I_1=X(0.07251)=797.50 \\ & X=10,999.02\end{aligned}[[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.