Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual...

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Finance

Paul Adams owns a health club in downtown Los Angeles. Hecharges his customers an annual fee of $950 and has an existingcustomer base of 690. Paul plans to raise the annual fee by 6percent every year and expects the club membership to grow at aconstant rate of 2 percent for the next five years. The overallexpenses of running the health club are $134,000 a year and areexpected to grow at the inflation rate of 2 percent annually. Afterfive years, Paul plans to buy a luxury boat for $590,000, close thehealth club, and travel the world in his boat for the rest of hislife. Assume Paul has a remaining life of 25 years and earns 9percent on his savings.

How much will Paul have in his savings on the day he starts hisworld tour assuming he has already paid for his boat? (Donot round intermediate calculations and round your answer to 2decimal places, e.g., 32.16.)

Account value at retirement

What is the annual amount that Paul can spend while on his worldtour if he will have no money left in the bank when he dies?(Do not round intermediate calculations and round youranswer to 2 decimal places, e.g., 32.16.)

Annual withdrawal

Answer & Explanation Solved by verified expert

3.8 Ratings (642 Votes)

1). Account value at retirement = 4,073,531.79

Formula	Year (n)	0	1	2	3	4	5
	Growth rate in number of customers (g1)		2%	2%	2%	2%	2%
Nn-1*(1+g1)	Number of customers (N)	690.00	703.80	717.88	732.23	746.88	761.82
	Growth rate for annual fee (g2)		6%	6%	6%	6%	6%
Afn-1*(1+g2)	Annual fee (AF)	950.00	1007.00	1067.42	1131.47	1199.35	1271.31
N*AF	Total revenue (TR)	655,500.00	708,726.60	766,275.20	828,496.75	895,770.68	968,507.26
	Growth rate of annual expenses (g3)		2%	2%	2%	2%	2%
Aen-1*(1+g3)	Annual expense (AE)	134,000.00	136680.00	139413.60	142,201.87	145,045.91	147,946.83
TR - AE	Net profit (NP)		572,046.60	626,861.60	686,294.87	750,724.77	820,560.43
NP*(1+9%)^(5-n)	Future value of net profit (FV)		807,490.46	811,803.95	815,386.94	818,290.00	820,560.43
Sum of all FVs	Total amount at retirement	4,073,531.79

2). Paul has another 20 years to live from the time he retires, so the annual withdrawal will be:

PV = 4,073,531.79; N = 20; rate = 9%; FV = 0; CPT PMT.

Annual withdrawal = 446,241.05

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Transcribed Image Text

Paul Adams owns a health club in downtown Los Angeles. Hecharges his customers an annual fee of $950 and has an existingcustomer base of 690. Paul plans to raise the annual fee by 6percent every year and expects the club membership to grow at aconstant rate of 2 percent for the next five years. The overallexpenses of running the health club are $134,000 a year and areexpected to grow at the inflation rate of 2 percent annually. Afterfive years, Paul plans to buy a luxury boat for $590,000, close thehealth club, and travel the world in his boat for the rest of hislife. Assume Paul has a remaining life of 25 years and earns 9percent on his savings.How much will Paul have in his savings on the day he starts hisworld tour assuming he has already paid for his boat? (Donot round intermediate calculations and round your answer to 2decimal places, e.g., 32.16.)Account value at retirement What is the annual amount that Paul can spend while on his worldtour if he will have no money left in the bank when he dies?(Do not round intermediate calculations and round youranswer to 2 decimal places, e.g., 32.16.)Annual withdrawal