Question 1062056: Correct Anwers?
You would like to have $750,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 4.2% 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?
You would like to have $750,000 when you retire in 25 years. How much should you invest each quarter if you can earn a rate of 4.2% compounded quarterly?
future value = (payment)[((1+i)^n-1)/i]
750000 = P[(1.042^(4*25)-1)/0.042]
750000 = P[1433.4]
payment = $523.23
a) How much should you deposit each quarter?:: 523.2307
b) How much total money will you put into the account?:: $52,323.07
c) How much total interest will you earn?:: 750,000-52323 = 697,676.93
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 750,000=A(1+(0.042/4)^100 minus 1)/(.042/4)
I will round here, but don't round until the end.
750,0008(0.042/4)=7875
7875=A (2.842-1)
A=7875/1.842=$4275.23
Every quarter for 25 years is 100 times that, or $427,523 deposited
The interest is 750,000-427523=$322,477.
The important thing is to divide the annual interest rate by the number of compoundings per year (here, 4) before raising it to the 100th power here, and dividing all that by 0.042/4. That is where the 7875 came from, 750,000*(0.042/4).
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