Question
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)
(Round to the nearest cent)
Answers
GPT 3.5
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.
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.