1. For purposes of compensation, an actuary working for a lawyer estimates the annual earnings of a September 11 victim that died at the Twin Towers at age 32. The victim was making $95,000 a year and a stream of payments for that amount would have likely accrued to her annually until retirement at age 65. The actuary knows that this is an ordinary annuity problem. He assumes, as is usual, that the victim's salary would grow in tandem with inflation, which for years has hovered at around 3% annually. What is the future value of this annuity, the minimum basis for a possible settlement with the relatives of the victim, if a fair settlement were indeed on the table?NOTE: Please note that, in court, the argument over compensation will likely be about the annuity's present value, as close relatives have immediate needs for cash; we will cover the concept of an annuity's present value next week and revisit this problem then.
2. A young, investing-savvy artistplansto retire in 30 years and is planning to save $1,000 every month. They plan to deposit the money at the beginning of each month into an account paying 5% compounded monthly. How much will they have in 30 years?
3. "The MacArthur Fellowship is a $625,000, no-strings-attached award to extraordinarily talented and creative individuals as an investment in their potential. There are three criteria for selection of Fellows: (1) Exceptional creativity; (2) Promise for important future advances based on a track record of significant accomplishments; and (3) Potential for the Fellowship to facilitate subsequent creative work. Each fellowship comes with a stipend of $625,000 to the recipient, paid out in equal quarterly installments over five years (therefore, $31,250 per quarter)." One of the recipients in 2019 was "Mary Halvorson, a guitarist, ensemble leader, and composer who is pushing against established musical categories with a singular sound on her instrument and an aesthetic that evolves with each new album and configuration of bandmates. She melds her jazz roots with elements of experimental rock, folk, and other musical traditions, reflecting a wide range of stylistic influences." Supposing that at the end of every quarter Mary is depositing the stipend she receives into an investment account that is paying an average annual return of 10% (similar to S&P 500 index). How much would Mary have at the end of the five years?