At time 0, Cheryl deposits X into a bank account that credits interest at an annual effective rate of 7%. At time 3, Gomer deposits 1000 into a different bank account that credits simple interest at an annual rate of y%. At time 5, the annual forces of interest on the two accounts are equal, and Gomer’s account has accumulated to Z.

Calculate Z.

• 1160
• 1200
• 1390
• 1400
• 1510

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

Solution: A

Cheryl’s force of interest at all times is ln(1.07) = 0.06766. Gomer’s accumulation function is from time 3 is 1 + yt and the force of interest is y/(1 + yt). To be equal at time 2, the equation is 0.06766 = y/(1 + 2y), which implies 0.06766 + 0.13532y = y for y = 0.07825. Gomer’s account value is 1000(1 + 2x0.07825) = 1156.5.

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