Xiaofei Li is only 30 years old, but he believes in planning ahead. His salary as a curator at the Financial Derivatives Museum is $70,000 p.a. He expects raises of 3% p.a. for the next five years. Then the director of the museum will retire and Xiaofei will get his job, with a pay raise of 30%. Thereafter he expects pay raises of 3% p.a. until he retires. He will save 5% of his salary for the first five years. He will save 7% of his salary for the next 15 years, until his house mortgage is paid off. Then he can save 20% of his salary each year. He saves in an RRSP and there is no tax on the 4% interest he earns on his savings. All savings are at the end of the year.

(a) How much will he have saved at age 55?

(b) If he retires at 60, he will need to have saved $800,000 for a comfortable retirement. How much more does he need to save each year from age 55, in addition to the 20% of his salary already given, to retire at 60, assuming the additional savings is an ordinary annuity, not a growth annuity?