Question

6. (14 pts) You are considering an investment in a 40-year security. The security willl pay $25a year at the end of cach of the rst 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 $800. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e, for 17 years)?

Answer 1

The present value approach can be used here

Current price of security= present value of all future cash flows

Cash flow after year 1 = C1 = $25 =C2 =C3

C4=C5=...= C23 = $30

C24= C25=....=C40 = X (say)

Therefore

800 = (25/1.08 + 25/1.08² + 25/1.08³) + (30/1.08⁴+....+30/1..08²³) + (X/1.08²⁴ +....+ X/1.08⁴⁰)

Applying the sum of GP formula

800 = 25/0.08 * {1-(1/1.08)³} + 30/0.08 *{1-(1/1.08)²⁰}/1.08³ + X /0.08 *{1-(1/1.08)¹⁷}/1.08²³

=> 800   = 64.43+ 233.82 + 1.553554X

=> 1.553554 X =501.75

=> X = $322.97

which is the equal payment to be received from year 24 through year 40 (17 years)