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 initial deposit that should be made today in order to accumulate to $9000 in three years at an interest rate of 4% compounded monthly, we can use the formula for compound interest:

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

Where:
A = the future value of the investment ($9000)
P = the principal or initial deposit we want to find
r = the interest rate per period (4% or 0.04)
n = the number of compounding periods per year (monthly compounding, so 12)
t = the number of years (3)

Plugging in the values:

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

We can simplify this equation:

9000 = P(1.003333...)^(36)

Now, divide both sides of the equation by (1.003333...)^(36):

P = 9000 / (1.003333...)^(36)

Using a calculator, we can find that (1.003333...)^(36) is approximately 1.1255. Therefore:

P = 9000 / 1.1255

P ≈ 7996.90

Therefore, an initial deposit of approximately $7996.90 should be made today in order to accumulate to $9000 in three years at an interest rate of 4% compounded monthly.