Question 1
Multiple ChoiceAn investment will make eight annual payments of $12,000 each, with the first payment beginning six years from today. If the appropriate discount rate is 7% per year, what is the present value of this annuity today?
Explanation
This is a deferred ordinary annuity. The present value is calculated in two parts:
Step 1: Calculate the PV at time = 5
This is a regular annuity with:
PMT = 12,000
N = 8
I/Y = 7%
FV = 0
Solve for PV (at time = 5)
BA II Plus Steps:
2nd → CLR TVM
N = 8
I/Y = 7
PMT = -12,000
FV = 0
CPT → PV ≈ 75,112.18
Step 2: Discount the PV back to today (time = 0)
Now take the PV of that lump sum (75,112.18) discounted 5 years at 7%:
PV = \frac{75,112.18}{(1 + 0.07)^{5}} = 59,822
Or using BA II Plus:
2nd → CLR TVM
N = 5
I/Y = 7
PV = ?
FV = 75,112.18
PMT = 0
CPT → PV ≈ 59,822