Svetlana won $1,000,000 in a contest, to be paid in twenty $50,000 payments at yearly intervals, the rst payment paid at the time of the contest. (of course, the present value of her winningis less than $1,000,000.) svetlana decided to keep x each year to spend and deposit theremaining $50,000-x into an account earning an annual eective interest rate of 5%. shechose the value x to be as large as possible so that, at the moment of the 20th deposit, theaccount would have grown to such a size that it would provide svetlana and her heirs at leastx per year in interest forever. find x.

The amount X she can retire out of every payment is $31,155.52.

Step-by-step explanation:

We start calculating the amount needed to provide an perpetuity of X after the 20th deposit. The formula for the the present value of a perpetuity is

This is the amount of capital she has to have in her account to provide X yearly forever.

We have 20 payments, which are compunded at an effective rate of 5%. The amount deposit out every payment is (50,000-X).

We can write a timeline to see all the deposits

We can express then the capitalization of the deposit (C) as

This capital C has to be equal to 20X:

Then, the amount X she can retire out of every payment is $31,155.52.

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

answer: (1,3) (3,-1) (5,-5) ?

step-by-step explanation: