Back to Assignment Average: /3 Attempts 7. Present value of annuities and annuit

Question

Back to Assignment Average: /3 Attempts 7. Present value of annuities and annuity payments The present value of an annuity is the sum of the discounted value of all future cash flows. Aa Aa You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. O An annuity that pays $500 at the end of every slx months O An annuity that pays $500 at the beginning of every sik months O An annuity that pays $1,000 at the beginning of each year O An annuity that pays $1,000 at the end of each year An ordinary annuity selling at $13,483.41 today promises to make equal payments at the end of each year for the next six years (N). If the annuity's appropriate interest rate (1) remains at 8.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won assuming annual interest rate of 8.00%. Grade It Now Save & Continue esc

Explanation / Answer

1) if we are paid 500 after every 6 months and paid 1000 after every 1 year, first option is better as in first case, we can reinvest the 500 (which we got after 6 months) and at the end of 1 year total annuity payout will definetly be more then $1000 (as there will be some interest gained due to investment for 6 months).

Also, earlier the annuity paid, better it is.

So out of options given, "An annuity that pays $500 at the beginning of every six months" is the best among the options listed.

2) Enter the following in the financial calculator to calculate the annual annuity payment.

PV = 13,483.41; n=6; 1/y = 8%; FV = 0; calculate PMT = $2916.61

3) Adjust the mode of financial calculator to 1 (i.e.cash flows are accounted for the beginning period)

Now, enter the following.

n=6; 1/y = 8%; FV = 0; PMT = $35 million / 6; calculate PV = $29,124,142

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