Course: Theory of Interest (Actuarial Science) Chapter: Yield Rates Problem: This is a Multi-Part Question Joe's retirement scheme...

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Course: Theory of Interest (Actuarial Science)
Chapter: Yield Rates
Problem: This is a Multi-Part Question
Joe's retirement scheme at work pays $500 at the end of eachmonth. Joe puts his money in an account which earns a nominal 12%converted monthly, the interest is reinvested at a nominal 4%converted monthly. Carol's account also pays $500 at the end ofeach month, but she earns nominal 12% convertible monthly(principal and interest both earn 12%). After 20 years, Joe andCarol retire.
a) How much money will Carol have? Answer: $184,465.8246
b) How long will it be before Carol's account exceeds Joe's by$1,000,000? Answer: 355.0933299 months or 29.59111082 years

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Below is he formula for an annuity where the reinvested at different rate is given below Accumulated Future Value A n i 1rn1r ni Where i coupon interest earned by investor A annuity amount n number of periods r reinvestment rate By using formula substituting the values Joes accumulated value after 20 years Future valueJoe 5002401 1033324010333324003333 Where i and r are See Answer

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