Joe's retirement scheme at work pays $500 at the end of each month. Joe puts his money in an account which earns nominal 12% converted monthly, the interest is reinvested at a nominal 4% converted monthly. Carol's account also pays $500 at end of each month, but earns nominal 12% convertible monthly (principal and interest both earn 12%). After 20 years, they retire. How much more money will Carol have? (ANSWER: $184,465.8246)

Same scenario above: How long until Carol's account exceeds Joe's by $1,000,000? (ANSWER:355.0933299months)