Question

Finding present value in Exercise, determine the principal P that must be invested at interest rate r, compounded continously, so that $1,000,000 will be available for retirement in t years.
r = 7.5%, t = 40

Answer 1

Answer:

$49,787.16

Step-by-step explanation:

The expression that describes continuous compounding is:

$FV = P*e^{rt}$

The principal (p) that yields a future value of $1,000,000 at a rate of 7.5% for 40 years is given by:

$1,000,000= P*e^{0.075*40}\\1,000,000=20.0855 P\\P=\ 49,787.16$

The principal value that must be invested is $49,787.16.