A 4-year annuity of eight $11,400 semiannual payments will begin 9 years from no
ID: 2382844 • Letter: A
Question
A 4-year annuity of eight $11,400 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.
If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
If the discount rate is 11 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Explanation / Answer
The cash flows in this problem are semiannual, so we need the effective semiannual rate. The interest rate given is the APR, so the monthly interest rate is: .09167
Semiannual rate = (1.009167)6 – 1 = .0563 or 5.63%
We can now use this rate to find the PV of the annuity. The PV of the annuity is:
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
PVA @ year 9: $11400{[1 – (1 / 1.0.0563)8] / .0.0563} = $71840.05
Discount the value (9 years from now) back 5years to get the value 4 years from now
n = 4yrs * 2 times per year =8,
PV = 71840.05 / 1.0563)^8=46351.96
n = 6yrs * 2 times per year =12,
PV = 71840.05 / 1.0563)^12=37232.22
another simple Method
The cash flows in this problem are semiannual, so we need the effective semiannual rate. The interest rate given is the APR, so the monthly interest rate is: .09167
Semiannual rate = (1.009167)6 – 1 = .0563 or 5.63%
We can now use this rate to find the PV of the annuity. The PV of the annuity is:
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
PVA @ year 9: $11400{[1 – (1 / 1.0.0563)8] / .0.0563} = $71840.05
Discount the value (9 years from now) back 5years to get the value 4 years from now
n = 4yrs * 2 times per year =8,
PV = 71840.05 / 1.0563)^8=46351.96
n = 6yrs * 2 times per year =12,
PV = 71840.05 / 1.0563)^12=37232.22