Question

Urgent please show to work problem!

To supplement your retirement income, you would like to receive an additional $30,000 per year for 20 years (with the first payment at the end of the year when you’re 60). You open an investment account when you are 20 years old. If the account yields 7.5% annually (and will continue to yield 7.5% through your retirement), how much must you invest each month for the next 40 years to meet your goal

Answer 1

Given that,

An constant annual withdrawal of $30000 per year is made for next 20 years.

So value at the time of retirement can be calculated using PV formula of annuity,

interest rate = 7.5%

PV = PMT*(1 - (1+r)^(-t))/r = 30000*(1 - 1.075^-20)/0.075 = $305834.74

Value of account at year 60 is $305834.74

Now formonthly deposit for 40 years,

So, monthly deposit can be calculated using FV formula of an annuity,

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 305834.74*(0.075/12)/((1+0.075/12)^(12*40) - 1) = $101.14

So, monthly deposit in account before retirement = $101.14