Revision as of 22:48, 17 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>1160</li><li>1200</li><li>1390</li><li>1400</li><li>1510</li></ul> {{soacopyright | 2023 }}")
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ABy Admin
Nov 17'23

Exercise

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.

ABy Admin
Nov 17'23

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.

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