Multiple Choice Question Primo, Inc. issued $$ \$ 50,000,5 $$-year, $$ 7 \% $$ bonds that pay interest annually on January 1 when the going market interest rate was $$ 6 \% $$. The issue (sale) price of the bonds equals the O present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,500 $$, both discounted at $$ 7 \% $$ and 5 periods. O present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,000 $$, both discounted at $$ 7 \% $$ and 5 periods. O present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,500 $$, both discounted at $$ 6 \% $$ and 5 periods. O present value of $$ \$ 53,500 $$ discounted at $$ 7 \% $$ and 5 periods.

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To determine the correct answer, we need to analyze the bond's characteristics and how to calculate its issue price based on the present value of future cash flows.

### Known Conditions:
1. **Face Value of Bonds (FV)**: $$ \$ 50,000 $$
2. **Coupon Rate**: $$ 7\% $$
3. **Annual Interest Payment**: $$ 7\% \times 50,000 = \$ 3,500 $$
4. **Market Interest Rate**: $$ 6\% $$
5. **Number of Periods (n)**: $$ 5 $$ years

### Steps to Calculate the Issue Price:
1. **Calculate the Present Value of the Face Value**:
   - The face value of the bond will be paid back at the end of the 5 years. We need to discount this amount back to present value using the market interest rate of $$ 6\% $$.

$$
   PV_{FV} = \frac{FV}{(1 + r)^n} = \frac{50,000}{(1 + 0.06)^5}
   $$

2. **Calculate the Present Value of the Annuity (Interest Payments)**:
   - The bond pays $$ \$ 3,500 $$ annually for 5 years. We need to calculate the present value of these annuity payments using the market interest rate of $$ 6\% $$.

$$
   PV_{Annuity} = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) = 3,500 \times \left( \frac{1 - (1 + 0.06)^{-5}}{0.06} \right)
   $$

3. **Total Present Value (Issue Price)**:
   - The total present value (issue price) of the bonds is the sum of the present value of the face value and the present value of the annuity.

$$
   Total\ PV = PV_{FV} + PV_{Annuity}
   $$

### Evaluating the Options:
Now, let's evaluate the options based on the calculations:

1. **Option 1**: Present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,500 $$, both discounted at $$ 7\% $$ and 5 periods.
   - Incorrect because the market rate is $$ 6\% $$.

2. **Option 2**: Present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,000 $$, both discounted at $$ 7\% $$ and 5 periods.
   - Incorrect because the annuity payment is $$ \$ 3,500 $$ and the market rate is $$ 6\% $$.

3. **Option 3**: Present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,500 $$, both discounted at $$ 6\% $$ and 5 periods.
   - Correct because it uses the correct annuity payment and the market rate.

4. **Option 4**: Present value of $$ \$ 53,500 $$ discounted at $$ 7\% $$ and 5 periods.
   - Incorrect because it misrepresents the cash flows.

### Conclusion:
The correct answer is:
**Present value of $$ \$ 50,000 $$ plus the present value of an annuity of $$ \$ 3,500 $$, both discounted at $$ 6\% $$ and 5 periods.**
The issue price of the bonds is the present value of \$50,000 plus the present value of an annuity of \$3,500, both discounted at 6% for 5 periods.

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