Edward deposits $250 each month into a retirement
account that pays 6.00% APR (0.50% per month). What is the value of this annuity after 20 years?
Edward deposits $250 each month into a retirement
account that pays 6.00% APR (0.50% per month). What is the value of this annuity after 20 years?
Since you are looking for the future value (in 20 years) of this annuity, there is a simple mathematical formula you can use to make this calculation. The formula is as follows:
FV = PMT * [ ((1 + i)^{n} - 1) / i ] , where
FV = future value
PMT = amount of periodic payment = $250 (per month)
i = interest rate (per month) = 0.50% / 100% = 0.005
n = # of compounding periods = 20 years * 12 months/year = 240 (payments for 20 years)
Plug in all these given values into the above formula:
FV = 250 * [ ((1 + 0.005)^{240} - 1) / 0.005 ]
= 250 * [ (1.005^{240} - 1) / 0.005 ]
= 115,510.22379037
≈ 115,510.22
Thus, the value of this annuity after 20 years is approximately $115,510.22
Academic honesty. I looked this formula up from text. It is too easy to make an error deriving it and I felt lazy.
P = A((1 + (i/q))^(n/q) - 1)(q/i)
where P is the principal after years
A is the amount deposited each interval (month)
i = interest rate (.06)
q = no. of pay periods/ year (12)
n = no of years. 20
= 115,510.22. Almost double the amount paid in (60000)