Question

Suppose that an amount in dollars, is invested in a private financial institution, with interest

compounded continuously at 8% per year.

a) Write the equation in terms of P, and 0.08 where P, is the starting amount

invested. And the final balance in the account is denoted with variable P

b) Suppose that $2000 is invested. What is the total amount in the account after 3

years?

c) How many years will it take to have more than the invested amount

Answer 1

Continuous compoynding is given by the equation:

$FV=P_oe^{rn}$

Where FV = future or final value

$P_o=$ present or initial value invested

e= rate of increase

r = interest rate

n = number of years

a)$FV=P_oe^{rn}$

e= 2.71828, n= 1, $P_0=FV=P$ , r= 0.08

$\therefore\frac{P}{P_o}=2.71828^{0.08×1}$

$\frac{P}{P_o}=2.71828^{0.08}$

b) Assume that P =$2000 and n= 3

$FV_3=2000(2.71828)^{0.08×3}$

$FV_3=\$2542.50$

c) From (a), $\frac{P}{P_o}=e^{rn}$

$P>P_o$ at $n+1$