$3,000 is deposited into an account paying 10% annually,to provide three annual withdrawals of $1,206.34 beginning in one year.How much remains in the account after the second payment has been withdrawn?
A) $1,326.97
B) $1,206.34
C) $1,096.69
D) $587.32

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity, we can calculate the initial deposit needed to provide three $1,206.34 withdrawals at 10% interest:

$1,206.34 = C * (1 - (1/1.10)^3) / 0.10

Solving for C, we get:
C = $3,000 / (1 - (1/1.10)^3) * 0.10
C ≈ $2,598.41

Therefore, $2,598.41 needs to be deposited initially to provide the three withdrawals of $1,206.34 with 10% interest.

After the first withdrawal of $1,206.34, the remaining balance in the account is:
$2,598.41 + $2,598.41*0.10 - $1,206.34 ≈ $2,190.33

After the second withdrawal of $1,206.34, the remaining balance in the account is:
$2,190.33 + $2,190.33*0.10 - $1,206.34 ≈ $1,096.69

Therefore, the answer is C, $1,096.69.

$3,000 Is Deposited into an Account Paying 10% Annually,to Provide