Six years from today you need $10,000. you plan to deposit $1,500 annually, with the first payment to be made a year from today,

Question

3 years ago

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Six years from today you need $10,000. you plan to deposit $1,500 annually, with the first payment to be made a year from today,

in an account that pays an 8% effective annual rate. your last deposit, which will occur at the end of year 6, will be for less than $1,500 if less is needed to reach $10,000. how large will your last payment be?

Mathematics

1 answer:

Novosadov [1.4K] · Answer 1 · 2022-02-06T13:10:27+03:00

Like this variation of the problem! :)

We calculate the future value of the 6 annual deposits of $1500 at 8%:
F=1500(1.08^6-1)/(0.08)=11003.89
Since the last payment is due on the day of withdrawal, he would have paid $1500 to get back $11003.89, i.e. with an excess of 1003.89.
Therefore his last payment is 1500-1003.89=$496.11