Question

Taylor has a retirement account that pays 4% per year compounded monthly. Every month for 20 years, Taylor deposits $444, with the first deposit at the end of month 1. The day the last deposit is made, the interest rate increases to 6% per year compounded monthly. During retirement, Taylor plans to make equal monthly withdrawals for 15 years, thus depleting the account. The first withdrawal occurs one month after the last deposit. How much can be withdrawn each month?

Answer 1

Taylor can withdrawn 1,374.20 dollars each month

Step-by-step explanation:

Timeline:

deposits of 444 for 20 years = withdrawals of X for 15 years

<-----/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/---\\-\-\-\-\-\-\-\-\-\-\-\->

We must calcualte amount to satisfy:

future value of his deposits = present value of his withdrawals

We first need to get the future value of the retirement account

and then the PMT this fund can do.

deposits future value:

`C * ((1+r)^(time) -1)/(rate) = FV\\`

C $ 444

time 240 (20 years x 12 months er year)

rate 0.003333333 ( 0.04 annual rate / 12 months = monthly rate)

`444 * ((1+0.003333333)^(240) -1)/(0.003333333) = FV\\`

FV $162,847.9340

withdrawals PMT:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $162,847.93

time 180

rate 0.005

`162847.93 / (1-(1+0.005)^(-180) )/(0.005) = C\\`

C $ 1,374.203