How much must be deposited into an account to generate a $2,400 payment every three months for the next four years if the account earns 10% compounded quarterly
$3,562.81
To calculate the amount that needs to be deposited into an account to generate a specific payment at regular intervals, we can use the formula for the present value of an annuity.
The formula for the present value of an annuity is:
PV = PMT * (1 - (1 + r)^-n) / r
Where:
PV = Present Value (the amount to be deposited)
PMT = Payment per period ($2,400)
r = Interest rate per period (10% per year compounded quarterly, so 2.5% per quarter)
n = Number of periods (4 years, which is 16 quarters)
Let's plug in the values and calculate:
PV = $2,400 * (1 - (1 + 0.025)^-16) / 0.025
PV = $2,400 * (1 - 0.541404) / 0.025
PV = $2,400 * 0.458596 / 0.025
PV = $2,400 * 18.3438
PV ≈ $44,025.12
Therefore, approximately $44,025.12 must be deposited into the account to generate a $2,400 payment every three months for the next four years, assuming an interest rate of 10% compounded quarterly.