a) Define a geometric annuity immediate with growth rate R. b) Give the formula for the present value of a geometric annuity due with growth rate R and n payments starting at $1 if the effective interest rate per period is r. Immelda buys a new pair of shoes at the start of every month for 1 years. The first pair costs $100 and each subsequent pair costs 2% more than the one before. The interest rate is 4% compounded monthly. c) How much does the final pair of shoes cost? d) How much money has she spent on shoes? (In other words, if she had saved her money instead of buying shoes, how much money would she have at the end of 1 years?)