Question

In: Finance

Beginning at age 30, Ms. Trinh invests $2,000 each year into an IRA account until she...

Beginning at age 30, Ms. Trinh invests $2,000 each year into an IRA account until she retires. When she retires, she plans to withdraw equal amounts each year that will deplete the account when she is 90. Find the annual amount she will receive if she retires at age 70 and the account pays 6% compounded annually.

Solutions

Expert Solution

Value of her deposits is:

FV of annuity = P * [ (1+r)^n -1 ]/ r
Periodic payment P= $                2,000.00
rate of interest per period r=
Rate of interest per year 6.0000%
Payment frequency Once in 12 months
Number of payments in a year                            1.00
rate of interest per period 0.06*12/12 6.0000%
Number of periods
Number of years                               40
Number of payments in a year                                  1
Total number of periods n=                               40
FV of annuity = 2000* [ (1+0.06)^40 -1]/0.06
FV of annuity =                309,523.93

her investment nest egg is $309,523.93

Her withdrawal will be:

Annuity payment= P/ [ [1- (1+r)-n ]/r ]
P= Present value 309,523.93
r= Rate of interest per period
Rate of interest per annum 6.0%
Payments per year 1.00
Rate of interest per period 6.000%
n= number of payments:
Number of years 20
Payments per year 1.00
number of payments 20
Annuity payment= 309523.93/ [ (1- (1+0.06)^-20)/0.06 ]
Annuity payment= 26,985.71

Her annual receipt is $26,985.71

Please rate.


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