Final answer:
To calculate the IRR for a zero-coupon bond with a face value of $1,000 and a current price of $485.20, payable in 10 years, we use the equation $485.20 = $1,000 / (1 + r)^{10} and solve for 'r'. There is an inverse relationship between bond prices and market interest rates.
Step-by-step explanation:
The internal rate of return (IRR) is the interest rate that makes the net present value of all cash flows from a particular investment equal to zero. For the zero-coupon bond in question, which will pay its face value of $1,000 in 10 years and is currently priced at $485.20, the IRR is the rate 'r' that satisfies the equation $485.20 = $1,000 / (1 + r)^{10}. We solve for 'r' using a financial calculator or software that can handle such calculations, as there is no simple algebraic solution.
To understand how bond prices react to changing market interest rates, it is important to note that when market interest rates rise, existing bonds with lower rates become less attractive and therefore decrease in value, selling for less than their face value. Conversely, as market interest rates fall, existing bonds with higher rates increase in value, selling for more than their face value. This inverse relationship between market interest rates and bond prices is fundamental to bond investing.