Questions

$(15$ pts $)$ Consider an individual with an exponential annual discount factor $in(0,1]$ and per$-$period utility $u(c)=c.$ Suppose the individual can receive $$100$ at:

$t=1($one year from now$),$

$t=2($ t wo years from now$),$

$t=3($three years from now$)$

$($a$)$ Write the present value of receiving $$100$ at each of these three time points, assuming $=0\mathrm{.}96.$

$($b$)$ Compare exponential discounting to standard compound interest in finance. In one or two sentences, discuss the conceptual similarity $($or difference$)$ in how future values are discounted back to the present.