Final answer:
The correct answer is option 3. The internal rate of return on Nathan's investment in a zero coupon bond which he bought for $485.19 and redeemed for $1,000 after 10 years is approximately 7.5%. This corresponds to option 3 among the given choices.
Step-by-step explanation:
The question at hand requires us to calculate the internal rate of return (IRR) for an investment in a zero coupon bond. Nathan bought a zero coupon bond in 2003 for $485.19 and redeemed it in 2013 for $1,000. The internal rate of return is the interest rate that makes the net present value of all cash flows from the investment equal to zero. To find the IRR, we use the formula:
Net Present Value (NPV) = Present Value (PV) of future cash flows - Initial Investment.
When NPV is set to zero:
0 = $1,000 / (1 + IRR)10 - $485.19
Where:
- $1,000 is the future value of the bond
- $485.19 is the price Nathan paid for the bond in 2003
- IRR is the internal rate of return we are trying to find
- 10 is the number of years Nathan held the bond
Using a financial calculator or an equivalent financial function in a spreadsheet software, we can solve for IRR and find that it is approximately 7.5%.
Hence, the correct option for Nathan's internal rate of return on this investment is 7.5%, which corresponds to option 3 in the given choices.