Steven Wong wishes to save for his retirement by depositing $1,200 at the beginning of each year for thirty years. Exactly one year after his last deposit, he wishes to begin making annual level withdrawals until he has made twenty withdrawals and exhausted the savings. Find the amount of each withdrawal if the effective interest rate is 5% during the first thirty years but only 4% after that.

Question

Brandon Schroeder

Business

4 March, 16:41

Steven Wong wishes to save for his retirement by depositing $1,200 at the beginning of each year for thirty years. Exactly one year after his last deposit, he wishes to begin making annual level withdrawals until he has made twenty withdrawals and exhausted the savings. Find the amount of each withdrawal if the effective interest rate is 5% during the first thirty years but only 4% after that.

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Litzy · Answer 1

The amount of annual withdrawal is $$6,159.75

Explanation:

First and foremost one needs to determine the future value of the annual savings of $1,200 i. e the future value of the annuity due using the below fv formula:

=fv (rate, nper,-pmt,-pv, type)

rate is the 5% effective interest

nper is the number of years the $1,200 would be deposited into the account, which is 30

pmt is the amount deposited yearly i. e $1,200

pv is the present worth of $1,200 deposited for 30 years, which is zero since it is not known

type is 1 for annuity due, zero for ordinary annuity

=fv (5%,30,-1200,0,1)

=$83,712.95

Thereafter we need to determine how much he can withdraw if he makes 20 withdrawals at 4% interest rate

=pmt (rate, nper,-pv, fv, type)

rate is 4%

nper is 20

pv is $83,712.95

fv is not known

type is zero since withdrawal begins a year after the last deposit i. e at year end

=pmt (4%,20,-83712.95,0,0) = $ 6,159.75