An investor pays 4000 today for a three-year investment that returns cash flows of 1400 at the end of each year. The cash flows can be reinvested at the positive annual effective interest rate of i. Using an annual effective rate of interest of 4%, the net present value of this investment is 0.

Calculate i.

• 2.5%
• 3.0%
• 3.5%
• 4.0%
• 7.0%

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

Solution: E

Solution: [math]4000\left(1.04^3\right)=1400\left[1+(1+i)+(1+i)^2\right][/math], or [math]i[/math] solves the quadratic equation: [math]i^2+3 i-0.2139=0[/math]. Thus, [math]i=6.97 \%[/math] because the other root is negative.

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