How much money should be deposited today in an account that earns 4.5% compounded monthly so that it will accumulate to $13,000 in 3 years?
(Round to the nearest cent)
To calculate the amount of money that should be deposited today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($13,000)
P = the principal investment (the amount to be deposited today)
r = the annual interest rate (4.5% or 0.045)
n = the number of times that interest is compounded per year (monthly, so n = 12)
t = the number of years (3)
Plugging in the given values, the formula becomes:
13,000 = P(1 + 0.045/12)^(12*3)
To solve for P, we divide both sides of the equation by (1 + 0.045/12)^(12*3):
P = 13,000 / (1 + 0.045/12)^(12*3)
P ≈ $11,128.96
Therefore, approximately $11,128.96 should be deposited today in order to accumulate to $13,000 in 3 years.