A45-year old man puts $1000 in a retirement account at the end of each quarter until he reaches the age of 60 and makes no further deposits. if the account pays 8% interest compounded quarterly, how much will be in the account when he retires at 65?

The account will have $292,526.3494 by the time he retired

Step-by-step explanation:

The expression for the total amount earned from the investment is;

A=P(1+r/n)^nt

where;

A=future value of investment

P=present value of investment

r=annual interest rate

n=number of periods

t=number of years

In our case;

P=deposits $1000 every 3 months for 15 years

A year has 4 periods

The present value, P=1000×4×15=$60,000

r=8%=8/100=0.08

n=4

t=(65-45)=20 years

replacing;

A=60,000(1+0.08/4)^(4×20)

A=60,000(1.02)^80

A=292,526.3494

The account will have $292,526.3494 by the time he retired

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.