# Solved Question: a. What is the present value of annuity of $3,000 per year Get premium Solution to all your Homework Assignments exclusively on writerkingdom. We have CFA/MBA writers to provide customized model answers to your every academic problem ## Description Question: 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: $\dpi{100} \small PV = PMT * [\frac{1 - 1/(1+r)^n}{r}]$ 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:

$\dpi{100} \small FV = PMT * \frac{(1+r)^n - 1}{r} * (1+r)$

FV = 5000 * (1.08^10 -1)/0.08 * 1.08 = \$78,227.44

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