How much money should be deposited today in an account that earns 4% compounded monthly so that it will accumulate to $9000 in three​ years?

Answer 1

To find the amount that should be deposited today, we can use the formula for compound interest:

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

Where:
A = final amount ($9000)
P = principal amount (the amount to be deposited today)
r = annual interest rate (4% or 0.04)
n = number of times interest is compounded per year (12, since it's compounded monthly)
t = number of years (3)

Substituting the given values into the formula:

$9000 = P(1 + 0.04/12)^(12*3)

Simplifying the equation further:

$9000 = P(1 + 0.003333)^36

Now, let's solve for P:

P = $9000 / (1.003333)^36
P ≈ $7588.38

Therefore, approximately $7588.38 should be deposited today in order to accumulate $9000 in 3 years with an interest rate of 4% compounded monthly.