You would like to have $1,000,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 6.1% compounded quarterly?a) How much should you deposit each quarter?$b) How much total money will you put into the account?$c) How much total interest will you earn?

a) To calculate how much you should deposit each quarter, we will use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r/n)^(nt) - 1] / (r/n)

Where: FV = future value of the annuity ($1,000,000) P = unknown (this is what we're solving for) r = annual interest rate (6.1% or 0.061) n = number of times interest is compounded per year (4, since it's quarterly) t = number of years the money is invested for (25)

Rearranging the formula to solve for P gives us:

P = FV * (r/n) / [(1 + r/n)^(nt) - 1]

Substituting the given values into the formula gives us:

P = $1,000,000 * (0.061/4) / [(1 + 0.061/4)^(4*25) - 1]

This gives us a quarterly deposit of approximately $3,388.89.

b) The total amount of money you will put into the account is simply the amount you deposit each quarter times the total number of quarters. There are 4 quarters in a year, so over 25 years, there are 4*25 = 100 quarters.

So, the total amount deposited is $3,388.89 * 100 =$338,889.

c) The total interest earned is the future value of the annuity minus the total amount deposited. So, the total interest is $1,000,000 -$338,889 = $661,111.