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.
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?
1 answer