You are considering an investment in a 40-year security

You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

First, you need to find the present value at the nominal interest rate of 8% of the $25 paid for the first three years.

$25 x 2.5771 = $64.4275

Then, we will find the present value of the $30 paid for the next 20 years.

$30 x 9.8181 x 0.7938 = $233.8082

Then, we will find the equal annual payment as follows: -

Both the current price and present value of all payment must be equal. Therefore,

$360.39 = $64.4275 + $233.8082+ X(9.1216)(0.1703)
$360.39 = $298.2357 + 1.5534X
$62.1543 = 1.5534X
X = $40