Question

Annuity A makes annual payments of $813.73 for each of the next 10 years, while annuity B makes annual payments of $500 per year forever. At what interest rate would you be indifferent between the two? At interest rates above/below this break-even rate, which annuity would you choose?

Answer 1

813.73/r*(1-1/(1+r)^10)=500/r
=>813.73*(1-1/(1+r)^10)=500
=>1-1/(1+r)^10=500/813.73
=>1/(1+r)^10=1-500/813.73
=>r=(1/(1-500/813.73))^(1/10)-1
=>r=10.00%

At rate of 10%, indifferent

At rate above 10% choose Annuity A
At rate below 10% choose Annuity B