Texts: A 25-year-old worker plans to retire at age 65. He believes that $800,000 is needed to retire comfortably. How much should be deposited now at 4% compounded monthly to meet the $800,000 retirement goal?
Retirement goal:
$800,000
Interest rate:
4% compounded monthly
Age at retirement:
65
Current age:
25
Amount to be deposited now to meet retirement goal:
Unknown
To calculate the amount to be deposited now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/retirement goal
P = the principal amount (amount to be deposited now)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, we have:
A = $800,000
r = 4% = 0.04 (decimal form)
n = 12 (compounded monthly)
t = 65 - 25 = 40 years
Substituting the values into the formula:
$800,000 = P(1 + 0.04/12)^(12*40)
Simplifying the equation:
$800,000 = P(1.00333333333)^(480)
To solve for P, we divide both sides of the equation by (1.00333333333)^(480):
P = $800,000 / (1.00333333333)^(480)
Using a calculator or spreadsheet, we can calculate the value of P to determine how much should be deposited now to meet the retirement goal of $800,000.