Layla wants the present value of her retirement to equal $500,000 and plans to make monthly deposits into an annuity for the next 30 years. If the annuity interest rate is 4 percent, calculate how much Layla should invest every month to reach her goal. Round the answer to the nearest whole number.
To calculate the monthly deposit Layla should invest to reach her goal of $500,000 in 30 years at an interest rate of 4%, we can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present value of the annuity ($500,000)
PMT = Monthly deposit
r = Interest rate per period (4% or 0.04)
n = Total number of periods (30 years * 12 months = 360 periods)
Substitute the known values into the formula:
$500,000 = PMT * [(1 - (1 + 0.04)^-360) / 0.04]
Simplify the formula:
$500,000 = PMT * [(1 - (1.04)^-360) / 0.04]
$500,000 = PMT * [(1 - 0.03141) / 0.04]
$500,000 = PMT * [0.96859 / 0.04]
$500,000 = PMT * 24.21475
PMT = $500,000 / 24.21475
PMT ≈ $20,646
Therefore, Layla should invest approximately $20,646 every month to reach her goal of $500,000 in 30 years with a 4% interest rate.