Bond Increase over time

This is a very easy question but I don’t completely understand the reasoning, can someone please clarify?

Question A $1000, 5%, 20-yr annual pay bond has a yield of 6.5%. If the yield remains unchanged, how much will the bond value increase over the next three years?

Answer: $13.62

When i calculate using TVM in my calculator i get $834.72 over 20 years. When I change N to 17, I get 848.34. I dont understand why the bond would increase as it seems to me that I got the higher number when at 17 years and then it decreased leading up to year 20.

Can you show it? I don’t get what you think. Anyway, I would try to explain why the bond value increases over time. Since the yield rate is greater than the coupon rate, obivously, the bond is sold at discount at the beginning (or any time before it reaches maturity if the yield rate remains unchanged). Then, that 1.5% yield (6.5%-5%) will go to the bond value every time the coupon is issued.

When the bond is issued at a discount, that means the price/PV is less than par. Over time, the price/PV will converge towards Par at maturity (ie increase over time).

When the bond is issued at a premium, the price/PV is higher than par. Over time, the price/PV will converge towards Par at maturity (ie decrease over time).

All you have to remember is that the price will converge towards par as the bond matures.

Remember, the price/PV of a bond is just the present value of the cash flows. The more time there is to maturity, the more the discount factor affects the present value. For example, a cash flow of 1000 10 years from now at yield=5% is 1000/(1.05)^10, whereas if it’s 7 years from now, it’s 1000/(1.05)^7. The cash flow’s present value is affected more by time. When time is zero(like when the bond matures), the pv of this example is 1000/(1.05)^0, which is just 1000 !

This is assuming the yield stays the same, remember we can use spot rates to value a bond, and spot rates can vary for a specific time period.

There is a concept of Amortization of Discount or Premium. The key thing to remember is that with the passage of time the bond value converges to par value at maturity. If a bond is issued at discount the then the value of the bond will increase to maturity and if the bond is issued at premium the value will decrease to maturity. This is known as Amortization of discount or premium. The question has asked you to calculate the increase in value over 3 years. Increase is justified because the bond is issued at discount as the time decrease the PV increases.