Sam, a 20-year-old graduate, has just found his first full-time job. An investment analyst suggests that he should try to have a substantial amount saved by the time of his planned retirement on his 65th birthday. According to the plan set out by the analyst, Sam should invest $5,000 on his 21st birthday then $2,000 on each birthday up to and including his 31". No further deposits are made but the money invested continues to earn interest until his 65th birthday. If the interest rate is 7.5% p.a., compounded annually, how much should Sam have in savings at age 65 under this plan?