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)?

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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