$1.$ You have an expected liability $($cash outflow$)$ of $$500,000$ in $10$ years, and you use a discount rate of $10\%.$

a$.$ How much would you need to set aside at the end of each year for the next $10$ years to cover the expected liability?

b$.$ How much would you need to set aside at the end of each year for the next $7$ years to cover the expected liability?