anonymous
  • anonymous
A perpetuity is similar to a decreasing annuity, except that the payments continue forever. A grateful alumnus decides to donate a permanent scholarship of $1440 per year. How much money should be deposited in the bank at 8% interest compounded annually in order to be able to supply the money for the scholarship at the end of each year?
Mathematics
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anonymous
  • anonymous
A perpetuity is similar to a decreasing annuity, except that the payments continue forever. A grateful alumnus decides to donate a permanent scholarship of $1440 per year. How much money should be deposited in the bank at 8% interest compounded annually in order to be able to supply the money for the scholarship at the end of each year?
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
Since it is compounded each year, and 1440 is then taken out, only 1440 needs to be the interest. We are assuming the minumum, so $1440 tops. This means that the relationship is: \[8/100 = 1440/x\] so \[x=1440/(8/100) = 1440(100)/8 = 144000/8 = 18000\] thus he needs to deposit 18000.

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