Lee is 26 and wants to retire at 65 with a retirement fund f

Lee is 26 and wants to retire at 65 with a retirement fund from which he can draw an interest income of 150,000 a year. He assumes he will have an average rate of return of 6%. He wants to know how much he needs to save each month to reach his goal and how inflation will affect his retirement savings. In order to earn $150,000 per year in interest, the balance of Lee\'s retirement account must be large enough that 6% of the balance is $150,000

Solution

ANSWER: assumption is that he will need $150,000 till perpetuity.

a) We will first find the the present value at the end of age 65 , that lee needs at 6% , that is $150,000 continously.

pv = amount / interest ( for perpetuity)

pv = $150,000 / 6% = $2,500,000

so at the end of age 65 he will need $2,500,000

now we need to find out the monthly payment.

i = 6% per year or 6% / 12 or 0.5% per month.

n = 65 - 26 = 39 years or 39 * 12 = 468 months

the present value found will be future value when we are finding the monthly payment needed to be saved by mr. lee.

monthly payment = future value(a/f,i,n) = 2,500,000(a/f,0.5%,468) = 2,500,000 * 0.00053643 = $1,341.07

so lee needs to save $1,41.07 per month , so that he gets $150,000 per year from the age of 65 till perpetuity.

in excel we will use the =-pmt function as =-pmt(6%/12,468,,2500000) = $1,341.07

b) buying power = amount / (1 + inflation ) ^ n

bp = 150,000 / (1 + 3%) ^ 39

bp = 150,000 / (1.03) ^ 39

bp = 150,000 / 3.167

bp = $47,363.0319

so his retirement savings will be drastically affected with 3% inflation as the savings per year will be $47,363.03