Suppose a 25 year old wanted to retire at age 70 with an annual income (taken out of their investments at the beginning of each year) of $100,000 at todays prices. They believe that the return they will earn on their funds while in retirement is 3% (EAR) in real terms. They expect to live to the end of their 90th year and want to leave $100,000 (at todays prices) for their heirs to put on a big funeral party and then travel to spread their ashes at various places around the world. Calculate the real amount (at todays prices) the individual would need to save each year in order accumulate their retirement nest egg. Assume they invest the funds at the end of each year. Assume initially that they believe they will earn a return of 5% (EAR) in real terms.

i. What would the annual amount be (at todays prices) given the retirement account balance required in part a(i) assuming they started contributing at the end of the year following their 25th birthday?

ii. Given this same required retirement account balance (a(i) assumptions), what would the annual amount be assuming the return they earned was only expected to be 4% (EAR) in real terms?

iii. Given this retirement account balance (a(i) assumptions), what would the annual amount be assuming they waited and started contributing at age 35? (return EAR to 5%)?