Revision as of 20:51, 18 November 2023 by Admin (Created page with "An actuary invests 1000 at the end of each year for 30 years. The investments will earn interest at a 4% annual effective interest rate and, at the end of each year, the interest will be reinvested at a 3% annual effective interest rate. Calculate the accumulated value of the investment at the end of the 30-year period. <ul class="mw-excansopts"><li>51,625</li><li>53,434</li><li>55,260</li><li>58,437</li><li>58,938</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
An actuary invests 1000 at the end of each year for 30 years. The investments will earn interest at a 4% annual effective interest rate and, at the end of each year, the interest will be reinvested at a 3% annual effective interest rate.
Calculate the accumulated value of the investment at the end of the 30-year period.
- 51,625
- 53,434
- 55,260
- 58,437
- 58,938
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
[[math]]
\left[40(I S)_{\overline{29} \mid 0.03}+30(1000)\right]=\left[40 \frac{\ddot{s}_{ \overline{29} \mid 0.03}-29}{0.03}+30(1000)\right]=53,433.89
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.