Meg's pension plan is an annuity with a guaranteed return of 7% per year (compounded quarterly). she would like to retire with a pension of $10,000 per quarter for 10 years. if she works 26 years before retiring, how much money must she and her employer deposit each quarter? hint [see example 5.] (round your answer to the nearest cent.)

$985.92

Step-by-step explanation:

In order to solve this question, we are going to use two formulas.

Present Value of an Annuity

To get the value of the pension of 10,000 per quarter for 10 years. And

Sinking funds Payments Formula

to get the Payment to be deposited each quarter during 26 years.

So for the first formula

n= number of periods = we need to know how many quarters in 10 years are. We know there are 4 quarters in a year, so 10 years multiplied by 4 is 40 quarters

n= 40

For i=interest rate= it is 7% compounded quarterly. There are 4 quarters so we divide by 4 and we get:

i=7%/4=1,75%

PMT= 10,000

and these 285,942.30 would be our future value in the sinking fund payment formula with:

n= 26 years *(4 quarters a year)= 104 quarters

i=1.75%

FV=$285,942.30

And $985.92 would have to be deposited every quarter during 26 years to get a payment of $10,000 per quarter for 10 years.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.