When an investor purchases a bond, they are essentially lending money to the issuer of the bond. In return, the issuer pays a fixed rate of interest, known as the coupon rate, to the investor over a specified period of time. At maturity, the investor receives the face value of the bond. However, in some cases, the bond may be callable or redeemable, which means that the issuer can buy back the bond before the maturity date.



Before determining the purchase price of the bond, we need to calculate the yield rate. This is the rate of return that the investor will receive on their investment. In this case, we are given that the yield rate is to be 5% effective, which means that the investor will earn a 5% rate of return over the life of the bond.



To calculate the purchase price of the bond, we need to use the present value formula. This formula calculates the present value of future cash flows, taking into account the time value of money and the yield rate.

PV = FV / (1 + r)^n

Where:
PV = Present Value
FV = Future Value (Face Value of the Bond)
r = Yield Rate
n = Number of Years until Maturity

In this case, we are given that the face value of the bond is `1000 and the annual dividends are 4%. The yield rate is 5% effective, and we are assuming that the bond has a maturity of 10 years.

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

PV = `1000 / (1 + 0.05)^10
PV = `613.91

Therefore, the purchase price of the bond is `613.91.



In conclusion, the purchase price of a bond with annual dividends can be calculated using the present value formula, taking into account the yield rate, face value, and time until maturity. By calculating the present value, investors can determine whether the bond is a good investment opportunity and make informed investment decisions.