We have learned about present value of an income stream $I(t)$; one may also reverse the derivation to determine

the future value of the income at a time $t=T.$ The future value element of $I(t)$ is

$dFV=e^{r(T-t)}I(t)dt$

assuming a continuous compounding at fixed interest rate $r.$

If you save for a child's college at a rate of $$5,000/$year starting at the child's birth, how much money will be

available when she is $20?$ Assume a fixed $5\%$ return on investments.

$FV=$$$500,000$

$FV=$$$100,000e$

$FV=$$$50,000e$

$FV=$$$50,000\sqrt[\phantom{2}]{e}$

$FV=$$$100,000$

$FV=$$$100,000(e-1)$