When the market interest rate for borrowing and lending is 3.5%, what is the present value (price) of a bond that promises to pay $5000 per year for 3 years? A) 4510 B) 4669 C) 14010 D) 4831

What you are valuing here

A bond that pays a fixed amount each year is an annuity. Its price today is found by discounting each promised payment back to the present using the market interest rate.

Discounting each $5000 payment at 3.5%

Use the present value formula for each year $t$: $$\text{PV} = \sum_{t=1}^{3} \frac{5000}{(1+0.035)^t}$$ Compute each term: $$\frac{5000}{1.035} \approx 4830.92$$ $$\frac{5000}{1.035^2} = \frac{5000}{1.071225} \approx 4666.37$$ $$\frac{5000}{1.035^3} = \frac{5000}{1.108717875} \approx 4509.71$$

Add them to get the bond price

$$\text{PV} \approx 4830.92 + 4666.37 + 4509.71 = 14006.99 \approx 14010$$ So the closest option is C) 14010.

Quick reasonableness check

If there were no interest (0%), the value would be $5000 \times 3 = 15000$. With a positive interest rate, the present value must be less than $15000$, so a value near $14010$ makes sense.