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?
To find the amount that should be deposited today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount ($9000)
P = principal amount (the amount to be deposited today)
r = annual interest rate (4% or 0.04)
n = number of times interest is compounded per year (12, since it's compounded monthly)
t = number of years (3)
Substituting the given values into the formula:
$9000 = P(1 + 0.04/12)^(12*3)
Simplifying the equation further:
$9000 = P(1 + 0.003333)^36
Now, let's solve for P:
P = $9000 / (1.003333)^36
P ≈ $7588.38
Therefore, approximately $7588.38 should be deposited today in order to accumulate $9000 in 3 years with an interest rate of 4% compounded monthly.
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 account ($9000 in this case)
P = the principal amount (the amount to be deposited today)
r = the annual interest rate (4% or 0.04)
n = the number of times the interest is compounded per year (12 monthly compounding in this case)
t = the number of years (3 years in this case)
We want to solve for P, so we can rearrange the formula:
P = A / (1 + r/n)^(nt)
Substituting the given values, we have:
P = $9000 / (1 + 0.04/12)^(12 * 3)
Now we can calculate this using a calculator or step-by-step.
P = $9000 / (1 + 0.00333)^(36)
P = $9000 / (1.00333)^(36)
P ≈ $9000 / 1.125487
P ≈ $8000.00
Therefore, approximately $8000 should be deposited today in order to accumulate to $9000 in three years at 4% compounded monthly.
To find out how much money should be deposited today in an account that earns 4% compounded monthly, we can use the formula for the future value of an investment:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (the amount to be deposited today)
r = interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, we are given:
FV = $9000
r = 4% = 0.04 (converted to decimal form)
n = 12 (compounded monthly)
t = 3 years
Let's plug in these values into the formula and solve for PV:
$9000 = PV * (1 + 0.04/12)^(12*3)
To solve this equation, you can rearrange it to find PV:
PV = $9000 / ((1 + 0.04/12)^(12*3))
PV = $9000 / (1.0033333)^36
Using a calculator, we can calculate PV:
PV ≈ $7,689.37
Therefore, approximately $7,689.37 should be deposited today in the account to accumulate to $9000 in three years.