Richard worked for Monnie Financial Services for five years. He left his vested pension benefits in the Monnie plan when he changed employers. When he retired from his present employer at age 65, Monnie gave him a choice between taking the vested pension benefits in the form of a lifetime annuity of $15,000 per year paid at the end of the year or a lump sum. Richard wants to compare the value of the annuity to the lump sum.

Assuming Richard lives for 15 years, the rate of interest is 7%, and the payment is taken at the end of the year, what is the minimum amount that his employer could offer for him to choose the lump sum instead of the annuity?

Assuming Richard lives for 15 years, the rate of interest is 7%, and the payment is taken at the beginning of the year what is the minimum amount that his employer could offer for him to choose the lump sum instead of the annuity?