Question 1120101
f = p * (1 + r) ^ n


f = future value
p = present value
r = interest rate per time period
n = number of time periods.


in your problem, this becomes:


p + 3000 = p * (1 + .10) ^ 2


subtract p from both sides of this equation to get:


3000 = p * (1 + .10) ^ 2 - p


factor out the p to get:


3000 = p * (1 + .10) ^ 2 - 1)


simplify to get:


3000 = p * .21


solve for p to get p = 3000 / .21 = 14285.71429.


that's your present value.


to confirm this is accurate, replace p in your equation with that to get:


p + 3000 = p * (1 + .10) ^ 2 becomes:


17285.71429 = 14285.71429 * (1 + .10) ^ 2, which becomes:


17285.71429 = 17285.71429, which is true.


this confirms the solution is correct.