Richard e-mailed me that he and monica differed about the impact of his extra spending over the past 15 years. he calculated it at about $3,000 a year. he said the total cost of $45,000 was well within his capability to make up. monica said the cost was much higher and asked that they compute it. they had been offered an investment of $20,000 that would pay $70,000 in 20 years. they want to know if they should take it. finally, richard could sign up for an annuity at work. it would cost $100,000 at age 65 and provide payments of $8,000 per year over his expected 17-year life span. he wants to know if it is attractive. the appropriate market rate of return on investments is 7 percent after tax. calculate what the $3,000-per-year deficit, had it been invested, would have amounted to at the end of the 15-year period.