This question requires you to complete two calculations, as well as to answer qu

Question

This question requires you to complete two calculations, as well as to answer questions related to those calculations. These calculations involve PV discounting and are designed to show both the mechanics and the power of discounting along with the time value of money. Complete the following two calculations: show work. Calculate the PV of a 20-year California lottery pot paying $50,000 annually at the discount rate of 10%. Is it $1 million, why or why not? Calculate the price of a three-year treasury bond/note paying 5% coupon on $1,000 face value at the discount rate of 3%. What type of bond is it, premium, par or discount?

Explanation / Answer

Formula for present value of an annuity = PV= A [ (1+k)n-1/k(1+k)n]

PV = Present value of fund

A = periodical installments =50,000 annually

k=interest rate=10% pa

n=periods=20 year

PV= 50,000*[(1.10)^20-1]/0.10(1.10)^20

=50,000*8.513=$425,641

So PV of the annuity is $425,641

It will not be $ 1 million as the annuity payment are in future and they are discounted @10% to calculate in present value of the annuity. The annuity present value factor @10% for 20 years is 8.513.

So the PV will be 8.513 times the annuity amount =$425,641

Treasury Bond valuation Year Interest +maturity Discount factor@3% PV of cash flows Year 1                                   50              0.9709                   48.54 Year 2                                   50              0.9426                   47.13 Year 3                             1,050              0.9151                960.90                   1,057 So the current price of Bond is $1,057 It is selling in premium as interest rate is higher than market rate

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