Final answer:
The value of an annuity is inversely related to the discount rate, meaning when the discount rate decreases from 10% to 5%, the value of an annuity with fixed payments increases, because future payments are discounted less and thus have a higher present value.
Step-by-step explanation:
The relationship between the value of an annuity and interest rates is that the present value of an annuity is inversely proportional to the interest or discount rate. When you bought an annuity with 13 annual payments of $10,000 at a discount rate of 10%, if the discount rate suddenly drops to 5%, the value of your investment increases. This is because at a lower discount rate, each of the annuity's payments is worth more in today's dollars, thereby increasing the total present value of the annuity.
If we consider bonds as an example, a bond paying 8% which was bought before interest rates rose will have lower present discounted value when the interest rates increase, leading to a decrease in the bond's selling price. Conversely, if the interest rate drops, the value of this bond would increase because the fixed coupon payments are more valuable.