Question 2 Not yet answered Points out of 10.00 p Flag question Use Table $$ 12-1 $$ of your text to find the future value of $$ \$ 1,300 $$ deposited at the BEGINNING of every three months, for 3 years if the bank pays $$ 12 \% $$ interest, compounded quarterly. Select one: a. $$ \$ 18,789.65 $$ b. $$ \$ 19,955.20 $$ c. $$ \$ 19,003.13 $$ o. d. $$ \$ 20,830.22 $$

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We are given quarterly deposits of $$ \$1300 $$ made at the beginning of each period for 3 years. The bank pays $$ 12\% $$ per year compounded quarterly. Let us calculate the future value of the annuity due.

1. Since interest is compounded quarterly, the periodic interest rate is
   $$
   i = \frac{12\%}{4} = 0.03.
   $$

2. The total number of deposits (periods) is
   $$
   n = 3 \text{ years} \times 4 \text{ quarters per year} = 12.
   $$

3. For an annuity due (payments at the beginning of each period), the future value is given by the formula
   $$
   \text{FV} = P \times \frac{(1 + i)^n - 1}{i} \times (1 + i)
   $$
   where $$ P $$ is the periodic deposit.

4. Substituting the known values:
   $$
   \text{FV} = 1300 \times \frac{(1.03)^{12} - 1}{0.03} \times 1.03.
   $$

5. First, calculate $$ (1.03)^{12} $$:
   $$
   (1.03)^{12} \approx 1.42576.
   $$

6. Then, compute the annuity factor:
   $$
   \frac{(1.03)^{12} - 1}{0.03} = \frac{1.42576 - 1}{0.03} = \frac{0.42576}{0.03} \approx 14.192.
   $$

7. Adjust for the annuity due by multiplying by $$ 1.03 $$:
   $$
   14.192 \times 1.03 \approx 14.61776.
   $$

8. Finally, compute the future value:
   $$
   \text{FV} \approx 1300 \times 14.61776 \approx 19002.09.
   $$

The calculated future value is closest to $$ \$19,\!003.13 $$.

Therefore, the correct answer is

$$ c. \, \$19,\!003.13 $$.
The future value is approximately \$19,003.13.

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