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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 have the same positive interest rate. a.An annuity that pays $500 at the beginning of every six months b.An annuity that pays $1,000 at the end of each year c.An annuity that pays $500 at the end of every six months d.An annuity that pays $1,000 at the beginning of each year

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Answer:

a.An annuity that pays $500 at the beginning of every six months

Explanation:

Annuities 1 to 4 gave the following Present values of which the first is the  highest. See attached for calculations

PV  

6,794.52  

6,144.19  

6,294.52  

6,758.65  

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  PV  

Annuity 1 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500  

DCF @ 10% 1 0.953462589 0.909090909 0.866784172 0.826446281 0.787985611 0.751314801 0.716350555 0.683013455 0.651227778 0.620921323 0.592025252 0.56447393 0.538204775 0.513158118 0.489277068 0.46650738 0.444797335 0.424097618 0.404361213 0.385543289  

PV 500 476.7312946 454.5454545 433.392086 413.2231405 393.9928055 375.6574005 358.1752777 341.5067277 325.6138888 310.4606615 296.0126262 282.236965 269.1023875 256.5790591 244.6385341 233.2536901 222.3986673 212.0488092 202.1806067 192.7716447  6,794.52  

Annuity 2  1000 1000 1000 1000 1000 1000 1000 1000 1000 1000            

DCF  0.909090909 0.8264 0.751 0.683 0.620921323 0.56447393 0.513158118 0.46650738 0.424097618 0.385543289            

PV  909.0909091 826.4 751 683 620.9213231 564.4739301 513.1581182 466.5073802 424.0976184 385.5432894            6,144.19  

Annuity 3  500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500  

DCF  0.953462589 0.909090909 0.866784172 0.826446281 0.787985611 0.751314801 0.716350555 0.683013455 0.651227778 0.620921323 0.592025252 0.56447393 0.538204775 0.513158118 0.489277068 0.46650738 0.444797335 0.424097618 0.404361213 0.385543289  

PV  476.7312946 454.5454545 433.392086 413.2231405 393.9928055 375.6574005 358.1752777 341.5067277 325.6138888 310.4606615 296.0126262 282.236965 269.1023875 256.5790591 244.6385341 233.2536901 222.3986673 212.0488092 202.1806067 192.7716447  6,294.52  

Annuity 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000            

DCF 1 0.909090909 0.8264 0.751 0.683 0.620921323 0.56447393 0.513158118 0.46650738 0.424097618            

PV 1000 909.0909091 826.4 751 683 620.9213231 564.4739301 513.1581182 466.5073802 424.0976184             6,758.65  

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