Question

colin is trying to decide whether he should make his ira contribution at the beginning of the year or at the end of the year. he wants to save $5,000 per year for 25 years in his ira that can earn 7% per year. what would be the difference in his account value if he made the payments at the beginning of each year rather than at the end?

Answer 1

The difference in his account value if he made the payments at the beginning of each year rather than at the end is $22,137.16

What is the difference between ordinary annuity and annuity due?

An annuity due has contributions  made at the beginning of the year whereas an ordinary annuity contributions are made  at the end of the year

FV(annuity due)=PMT*(1+r)^N-1/r*(1+r)

FV(ordinary annuity)=PMT*(1+r)^N-1/r

PMT=yearly payment=$5,300

r=rate of return=7%

N=number of years=25

FV(annuity due)=$5000*(1+7%)^25)-1 ))*(1+7%)

FV(annuity due)=$338,382.35

FV(ordinary annuity)=$5,000*(1+7%)^25/7%

FV(ordinary annuity)=$316,245.19

FV(annuity due)-FV(ordinary annuity)=$338,382.35-$316,245.19

FV(annuity due)-FV(ordinary annuity)=$22,137.16

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