Question

What is the value of a zero-coupon bond that matures in 15 years if it promises to pay $5,000 at maturity, assuming an interest rate of 7.5 percent compounded annually?

Answer 1

The present value of a zero-coupon bond that promises to pay $5,000 in 15 years with a 7.5% annual interest rate is approximately $1,696.65.

Step-by-step explanation:

The value of a zero-coupon bond that matures in 15 years, which promises to pay $5,000 at maturity, can be calculated using the present value formula for a zero-coupon bond. This formula is:

PV = F /
`(1 + r)^n`

Where:

• PV is the present value of the bond,
• F is the face value of the bond,
• r is the annual interest rate (expressed as a decimal),
• n is the number of years until maturity.

Using the formula, the calculation for the present value with a 7.5 percent annual interest rate compounded annually is:

PV =
`5000 / (1 + 0.075)^1^5`

Performing this calculation:

PV =
`5000 / (1.075)^1^5`

PV = 5000 / 2.94504

PV = $1,696.65

Therefore, the value of the bond today is approximately $1,696.65.