Revision as of 12:02, 18 November 2023 by Admin (Created page with "A two-year loan of 100 is repaid with a payment of X at the end of the first year and 2X at the end of the second year. The annual effective interest rate charged by the lender is 8% in the first year and i in the second year. The annual effective yield rate for the lender is 10%. Calculate i. <ul class="mw-excansopts"><li>12.8%</li><li>12.9%</li><li>13.0%</li><li>13.1%</li><li>13.2%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A two-year loan of 100 is repaid with a payment of X at the end of the first year and 2X at the end of the second year. The annual effective interest rate charged by the lender is 8% in the first year and i in the second year. The annual effective yield rate for the lender is 10%.
Calculate i.
- 12.8%
- 12.9%
- 13.0%
- 13.1%
- 13.2%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: E
Based on the effective yield rate, After one year, the outstanding loan balance is 100 + 8 – 39.03 = 68.97. For the balance to be zero after two years,
[[math]]
68.97(1+i)-2(39.03)=0\Rightarrow i=78.06/68.97-1=0.1318=13.29 \%
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.