a. What is the present value of annuity of $3,000 per year, with the first cash flow received four years from today and the last one received 22 years from today if the discount rate is 8%?
b. What is the future value of an annuity of $5,000 per year, with the first cash flow being received today and lasting for 10 years (10 total payments of $4,000) if the interest rate is 8% annual.
a) This is a “delayed annuity” case
Number of payments = 19, PMT = $3,000
r = 8%
PV at end of year 3:
PV3 = $28,810.797
PV0 = PV3 * (1.08)-3 = $22,870.94
Therefore, PV of the delayed annuity = $22,870.94
b) This is an ‘annuity due’ problem because the first cash flow is received today. In ‘annuity due’ payments or receipts occur at the beginning of each period.
Formula for FV:
FV = 5000 * (1.08^10 -1)/0.08 * 1.08 = $78,227.44