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?
To solve this, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = number of years
In this case,
A = $13,000
r = 4.5% or 0.045 (decimal)
n = 12 (compounded monthly)
t = 3
Plugging in all the values, the formula becomes:
$13,000 = P(1 + 0.045/12)^(12*3)
Simplifying,
$13,000 = P(1.00375)^(36)
Now we can solve for P by dividing both sides of the equation by (1.00375)^36.
P = $13,000 / (1.00375)^36
Using a calculator, or any software with a power function, we can simplify further:
P ≈ $11,343.72
Therefore, approximately $11,343.72 should be deposited today in the account.