# Answer to Question #58211 in Finance for abdiaziz

Question #58211

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)?

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)?

Expert's answer

CF 0= 0 (press 0 cfj) CF 1-3 = 25 (press 25, press CFj, then press 3, press shift, press CFj) CF 4-23 = 30 (press 30, CFj, 20, shift, CFj) press 8, I, then press shift PRC.

Solve for NPV = $298.25. (this is the present value of the first 23 payments).

Difference between the security's price and PV of payments: $360.39 - $298.25 = $62.14.

Calculate the FV of the difference between the purchase price and PV of payments, Years 1-23: N = 23 I = 8 PV = -62.14 Solve for FV = $364.85. Calculate the value of the annuity payments in Years 24-40: N = 17 I = 8 PV = -364.85. Solve for PMT = $40.

Solve for NPV = $298.25. (this is the present value of the first 23 payments).

Difference between the security's price and PV of payments: $360.39 - $298.25 = $62.14.

Calculate the FV of the difference between the purchase price and PV of payments, Years 1-23: N = 23 I = 8 PV = -62.14 Solve for FV = $364.85. Calculate the value of the annuity payments in Years 24-40: N = 17 I = 8 PV = -364.85. Solve for PMT = $40.

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