Question

A 15-year annuity of thirty $7,000 semiannual payments will begin 10 years from now, with the first payment coming 10.5 years from now.

a. If the discount rate is 11 percent compounded monthly, what is the value of this annuity 5 years from now?

b. What is the current value of the annuity?

Answer 1

a. Effective semi annual rate, r = (1 + 0.11/12)^6 - 1

r = 0.05627592806

n = 30

PMT = 7,000

This formula gives the PV as of year 10

PV5 = PV/(1 + r)^(5 * 2)

PV5 = 100,318.3390362021/(1 + 0.05627592806)^10

PV5 = 100,318.3390362021/1.7289157305

PV5 = $58,023.8453884564

The value of this annuity 5 years from now is $58,023.8453884564

b. The current value, P0 = PV5/(1 + r)^(5 * 2)

P0 = 58,023.8453884564/(1 + 0.05627592806)^10

P0 = 58,023.8453884564/1.7289157305

P0 = $33,560.8291166834

The current value of the annuity is $33,560.8291166834