Question 1141723: A college savings account is constructed so that $1000 is placed in the account on January 1st of each year with a guaranteed 3% yearly return in interest, applied at the end of each year to the balance in the account. If this is repeatedly done, how much money is in the account after the $1000 is deposited at the beginning of the 19th year? Show the sum that leads to your answer as well as relevant calculations.
I get that a1 is 1000 and n is 19 but how do I find r?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! A college savings account is constructed so that $1000 is placed in the account on January 1st of each year with a guaranteed 3% yearly return in interest, applied at the end of each year to the balance in the account. If this is repeatedly done, how much money is in the account after the $1000 is deposited at the beginning of the 19th year? Show the sum that leads to your answer as well as relevant calculations.
I get that a1 is 1000 and n is 19 but how do I find r?
When deposits/payments are made at the BEGINNING of a period (month, year, quarter, etc.), we have what is called an ANNUITY DUE, instead of an
ORDINARY ANNUITY (an annuity consisting of deposits/payments made at the END of each period). As such, we use the formula for the FUTURE VALUE
of an ANNUITY DUE, which will result in the amount: 
In other words, the above includes 1 ADDITIONAL year's interest, added to the FUTURE-VALUE ORDINARY ANNUITY amount!!
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