Saving for retirement by contributing the same amount each month from your 23rd birthday until your 65th birthday, in an account that pays a steady 4% annual interest compounded monthly.
How much will be in your fund at age 65 if you save $100 a month?
monthly rate = .04/12 = .003333...
time from 23rd to 65th birthday = 504 months
amount = 100( 1.003333..^504 - 1)/.003333..
= $130,517.61
To calculate the amount in the retirement fund at age 65, we can use the formula for the future value of an ordinary annuity:
Future Value = P * ((1 + r)^nt - 1) / r
Where:
P = Monthly contribution amount ($100)
r = Annual interest rate (4% / 12)
n = Number of compounding periods per year (12)
t = Number of years (65 - 23 = 42)
Let's substitute the values into the formula and calculate:
P = $100
r = 4% / 12 = 0.04 / 12 = 0.00333 (rounded)
n = 12
t = 42
Future Value = $100 * ((1 + 0.00333)^(12*42) - 1) / 0.00333
Calculating this, the future value of the retirement fund at age 65 will be approximately $176,694.73.