Calculating Retirement Account Balance
You plan on retiring in 25 years. In order to increase your retirement income, you open a retirement account today, and make a $20,000 deposit. In addition, you will deposit $5,000 every year for the next 25 years. Your plan is to start making annual withdrawals of $50,000 from the account, after you retire. Assuming the account is earning 7% rate of interest, how many years will it take, after you retire, before the funds in your account are completely exhausted? Please include a written answer in a text box. (assume annual compounding)
To calculate the number of years it will take for the funds in the retirement account to be completely exhausted, we need to use the future value formula for an annuity:
FV = PMT x ((1 + r)^n – 1) / r
where FV is the future value of the annuity, PMT is the annual payment, r is the annual interest rate, and n is the number of payments.
Using the given values, we can calculate the future value of the annuity:
PMT = $5,000 r = 7% n = 25 PV = $20,000
FV = PMT x ((1 + r)^n – 1) / r + PV x (1 + r)^n FV = $5,000 x ((1 + 0.07)^25 – 1) / 0.07 + $20,000 x (1 + 0.07)^25 FV = $390,227.64
This means that after 25 years of contributions, the retirement account will have a balance of $390,227.64.
Now, let’s calculate how many years the funds will last if you withdraw $50,000 per year:
Withdrawal amount = $50,000 FV = $390,227.64 r = 7%
Using the formula for the present value of an annuity:
PV = PMT x (1 – (1 + r)^-n) / r
where PV is the present value of the annuity, PMT is the annual payment, r is the annual interest rate, and n is the number of payments.
We can solve for n to find out how many years the funds will last:
n = -ln(1 – PV x r / PMT) / ln(1 + r) n = -ln(1 – $390,227.64 x 0.07 / $50,000) / ln(1 + 0.07) n = 14.32
