What is the present value of a $1000 bond which pays $50 a year for 10 years, starting one year from now? Assume interest rate is 6% per year, compounded annually
PV = 50 [ 1 - 1.06^-10]/.06 + 1000(1.06)^-10
= 926.40
To calculate the present value of a bond, we need to discount the future cash flows (i.e. the coupon payments) to their present value using the given interest rate.
In this case, we have a bond with a face value of $1000 that pays $50 per year for 10 years, starting one year from now. The interest rate is 6% per year, compounded annually.
To calculate the present value of each cash flow, we can use the formula for the present value of an ordinary annuity:
PV = C * (1 - (1 + r)^(-n)) / r,
where PV is the present value of the annuity, C is the cash flow per period, r is the interest rate per period, and n is the number of periods.
In this case, C = $50, r = 6% (0.06), and n = 10.
Let's plug in the values and calculate the present value.
PV = $50 * (1 - (1 + 0.06)^(-10)) / 0.06
PV ≈ $50 * (1 - 0.55839) / 0.06
PV ≈ $50 * 0.44161 / 0.06
PV ≈ $367.73.
Therefore, the present value of the $1000 bond is approximately $367.73.