Question

Mary makes 10 annual deposits of $1000 each into an account. Beginning one year after the first deposit she receives a check for 6% of the value of this account. She deposits these checks into an account that earns interest at 4%. Find the total value of her accounts one year after she makes the last $1000 deposit.

Answer 1

In 1st year , deposit = $1000

In 2nd year, deposit = $1000, total amount=$2000, check amount=6/100*1000=$60, interest = 4/100*60 = $2.4, total amount in other account=$62.4

In 3rd year, deposit = $1000, total amount = $3000, check amount= 6/100*2000 =$120,amount in other account=$120+62.4 = $182.4, interest = 4/100*182.4=$7.296 , total amount in other account=$189.696

In 4th year, deposit=$1000, total amount = $4000, check amount=6/100*3000 =$180, amount in another account= $180+189.696 = $369.696 , interest = 4/100*369.696=$14.788, total amount in other account=$384.484

In 5th year, deposit=$1000, total amount=$5000, check amount=6/100*4000=$240, amount in other account=$624.484 ,interest=4/100*624.484=$25, total amount in other account= $649.4

In 6th year, deposit=$1000, total amount=$6000, check amount=6/100*5000=$300, amount in other account= $949.4, interest=4/100*949.4=$37.976, total amount in other account=$987.376

In the 7th year, deposit=$1000, total amount=$7000, check amount =6/100*6000=$360, amount in other account=$1347.376, interest=4/100*1347.376=$53.895, total amount in other account=$1401.27

In the 8th year, deposit=$1000, total amount=$8000, check amount=6/100*7000=$420, amount in other account=$1821.27, interest=4/100*1821.27=$72.85, total amount in other account=$1894.12

In the 9th year, deposit=$1000, total amount= $9000, check amount=6/100*8000=$480, amount in other account=$2374.12, interest=4/100*2374.12=$94.96, total amount in other account=$2469.08

In the 10th year, deposit= $1000, total amount=$10,000, check amount=6/100*9000=$540, amount in other account=$3009.08, interest=4/100*3009.08=$120.36, total amount in other account=$3129.44

In the 11th year, deposit=$1000, total amount in 1st account=$10,000, check amount=6/100*10,000=$600, amount in other account=600+3129.44=$3729.44, interest=4/100*3729.44=$149.18, total amount in other account= $3878.62