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an individual has $1,100,000 in a retirement account. at the beginning of each m

ID: 2649843 • Letter: A

Question

an individual has $1,100,000 in a retirement account. at the beginning of each mint she plans to withdraw $10,000 for the next 30 years depleting the account, what annual rate of return is she expecting? if she is only able to earn 8% a year on her money, when will she run out? an individual has $1,100,000 in a retirement account. at the beginning of each mint she plans to withdraw $10,000 for the next 30 years depleting the account, what annual rate of return is she expecting? if she is only able to earn 8% a year on her money, when will she run out? an individual has $1,100,000 in a retirement account. at the beginning of each mint she plans to withdraw $10,000 for the next 30 years depleting the account, what annual rate of return is she expecting? if she is only able to earn 8% a year on her money, when will she run out?

Explanation / Answer

This an annuity due. We can use PV of annuity due formula to calculate monthly rate of return.

PV = 1100,000

N = 30 x12 = 360

PMT =10,000

PV of annuity due = PMT + (PMT x PVIFA( N, R))

                1100,000 = 10,000+ 10,000 x PVIFA ( 360, R)

Solving for R, we get:

R= 0.8687% Here R is monthly rate. Annual rate of return would be:

Annual rate of return = 0.8687% x12

                                           = 10.42%

If she is able to earn 8%, then we need to calculate N using the same formula:

PV = 1100,000

R = 8%/12=0.67%

N = 30 x12 = 360

PMT =10,000

PV of annuity due = PMT + (PMT x PVIFA( N, R))

                1100,000 = 10,000+ 10,000 x PVIFA ( N, 0.67%)

Solving for N we get:

N =198.92 months or 198.92/12 =16.58 years.