Bob and Joy Salkind want to save $50,000 in 5 ½ years for home improvement projects. If the Bank of Aventura is paying 8% interest compounded quarterly, how much must the couple deposit now to have the money for the projects?

Ms. Sue Please don't post on the question unless you intend to HELP. Don't need the answer just asking for help with the equation, Thank You!!

To calculate the amount the couple must deposit now to have $50,000 in 5 ½ years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($50,000)
P = the principal amount (the amount to be deposited now)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (quarterly, so 4 times)
t = the number of years (5 ½ years)

Plug in the values into the formula and solve for P:

$50,000 = P(1 + 0.08/4)^(4 * 5.5)

Simplifying the equation:

$50,000 = P(1 + 0.02)^(22)

$50,000 = P(1.02)^22

Now, we divide both sides of the equation by (1.02)^22 to isolate P:

P = $50,000 / (1.02)^22

Using a calculator to perform the necessary calculations, we find:

P ≈ $33,107.61

So, Bob and Joy Salkind must deposit approximately $33,107.61 now to have $50,000 in 5 ½ years for their home improvement projects.

To find out how much Bob and Joy Salkind must deposit now to have $50,000 in 5 ½ years, we need to use the formula for compound interest, which is given by:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (in this case, $50,000)
P = the principal amount (the amount Bob and Joy must deposit now)
r = the annual interest rate (8% in this case)
n = the number of times interest is compounded per year (quarterly, so n = 4)
t = the number of years (5 ½ years)

By using this formula, we can rearrange it to solve for P:

P = A / ((1 + r/n)^(nt))

Substituting the given values, we have:

P = $50,000 / ((1 + 0.08/4)^(4 * 5.5))

Now let's calculate it:

Please do not post any more questions until you've gone back and explained what you don't understand in the previous questions.