Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 a quarter for 10 years. Assuming Mike's account earns 8% compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal

  $2398.52

Step-by-step explanation:

The amortization formula can be used to find the principal amount that is required to support payments of $10,000 per quarter.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

A is the periodic payment, P is the principal amount, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

  10,000 = P(.08/4)/(1 -(1 +.08/4)^(-4·10)) = .02P/(1 -1.02^-40)

  P = 10000(1 -1.02^-40)/.02

  P = $273,554.79 . . . . . balance required when payouts start

__

The annuity formula can be used to find the periodic payment required to achieve this balance.

  A = P((1 +r/n)^(nt) -1)/(r/n)

A is the sum of the payments P made n times per year. Interest rate r is also compounded n times per year for t years.

  273,554.79 = P((1 +.08/4)^(4·15) -1)/(.08/4) = P(1.02^60 -1)/.02 = 114.05154P

  273,554.79/114.05154 = P = 2398.52

Mike must deposit $2398.52 quarterly to accomplish his goal.

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.

the barter