Question

a $2,700 face-value bond (face-value is the amount you get paid when you cash it in after maturity) pays dividends of $270 at the end of each year. if the bond matures in 20 years, what is the approximate bond value at an interest rate of 4% per year, compounded annually? (approximately how much should you pay for this bond?)

Answer 1

The approximate bond value at an interest rate of 4% per year, compounded annually, is $4,823.76.

To calculate the approximate bond value at an interest rate of 4% per year, compounded annually, we can use the present value formula.

The formula is: Bond Value =
`Dividends / (1 + Interest Rate) + Dividends / (1 + Interest Rate)^2 + ... + Bond Face Value / (1 + Interest Rate)^n`, where n is the number of years to maturity. In this case, the bond pays dividends of $270 per year for 20 years, and the interest rate is 4%.

Using the formula, we can calculate the present value of the bond as follows:

Year 1: $270 / (1 + 0.04)^1 = $270 / (1.04) = $259.62

Year 2: $270 / (1 + 0.04)^2 = $270 / (1.0824) = $249.27...

Year 20: $270 / (1 + 0.04)^20 = $270 / (1.9252) = $79.17

Face Value: $2,700 / (1 + 0.04)^20 = $2,091.17

Summing up all the present values, the approximate bond value at an interest rate of 4% per year, compounded annually, is $4,823.76.