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.
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.
1 answer