find the present value for $2000 if interest is 3.5% compounded quarterly for 6 years?

i = .035/4 = .00875

n = 4x6 = 24

PV = 2000(1.00875)^-24
= .....

you do the button-pushing

24.084

To calculate the present value of an amount in the future, we need to use the formula for compound interest. The formula for compound interest is:

PV = FV / (1 + r/n)^(n*t)

where:
PV = Present value
FV = Future value
r = Interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years

In this case:
FV = $2000
r = 3.5% or 0.035 (as a decimal)
n = 4 (since it's compounded quarterly)
t = 6 years

Now let's substitute the values into the formula and calculate the present value:

PV = 2000 / (1 + 0.035/4)^(4*6)

First, let's simplify the expression inside the parentheses:

PV = 2000 / (1 + 0.00875)^(24)

Next, let's calculate 1 + 0.00875:

PV = 2000 / (1.00875)^(24)

Now, let's calculate (1.00875)^(24):

PV = 2000 / (1.235254)

Finally, let's divide $2000 by 1.235254 to find the present value:

PV ≈ $1618.09

Therefore, the present value of $2000, with an interest rate of 3.5% compounded quarterly for 6 years, is approximately $1618.09.