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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)?
a. $35
b. $38
c. $40
d. $45
e. $50
Expert Solution
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
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