Annuities and compounding
Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%.
a. Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if
(1) $300 is deposited annually and the credit union pays interest annually.
(2) $150 is deposited semiannually and the credit union pays interest semiannually.
(3) $75 is deposited quarterly and the credit union pays interest quarterly.
b. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)