Use present value equation.
If present value of annuity equals 400,000, then you are indifferent.
[tex]PV = A(v + v^2 + ...v^{20}) \\ \\ PV = A\frac{v(1-v^{20})}{1-v}[/tex]
where v = 1/(1+r) and A = annual payment = 800,000/20 = 40,000
PV = 400,000
After subbing in the numbers, the equation is:
[tex]10 = \frac{v(1-v^{20})}{1-v} \\ \\ 10 - 10v = v - v^{21} \\ \\ v^{21} - 11v+10 = 0 \\ \\ v = 0.928034 \\ \\ \frac{1}{1+r} = 0.928034 \\ \\ r = 0.0775[/tex]
Therefore at interest rate of about 7.75% you are indifferent.
