Question
Determine the face value of a zero coupon bond whose maturity is 3 years, its IRR is 4% and has a present value of $8,420
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Answer to a math question Determine the face value of a zero coupon bond whose maturity is 3 years, its IRR is 4% and has a present value of $8,420
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4.673 Answers
1. The formula for the present value (PV) of a zero-coupon bond is given by:
PV = \frac{FV}{(1 + r)^n}
where:
- \(PV\) is the present value
- \(FV\) is the face value
- \(r\) is the interest rate (IRR)
- \(n\) is the number of years to maturity
2. Rearrange the formula to solve for the face value \(FV\):
FV = PV \times (1 + r)^n
3. Substitute the given values into the formula:
FV = 8,420 \times (1 + 0.04)^3
4. Perform the calculation:
FV = 8,420 \times (1.04)^3
FV = 8,420 \times 1.124864
FV \approx 9478.40
Answer:FV \approx 9478.40
where:
- \(PV\) is the present value
- \(FV\) is the face value
- \(r\) is the interest rate (IRR)
- \(n\) is the number of years to maturity
2. Rearrange the formula to solve for the face value \(FV\):
3. Substitute the given values into the formula:
4. Perform the calculation:
Answer:
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