Today’s deposit of 9550 earns an annual effective interest rate of i for five years. At the end of the fifth year, the entire accumulated balance is reinvested into a 20-year annuity-due. The annuity-due has level annual payments of 756.97 at an annual effective interest rate of 4%.

Calculate i.

• 1.5%
• 2.3%
• 7.7%
• 12.0%
• 19.7%

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

Solution: B

[[math]] \begin{aligned} & 9550(1+i)^5=756.97 \ddot{a}_{2000.04} \\ & 9550(1+i)^5=10,698.97 \\ & (1+i)^5=1.12031 \\ & i=0.02298\end{aligned} [[/math]]

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