Question

Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $950 and has an existing customer base of 690. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of 2 percent for the next five years. The overall expenses of running the health club are $134,000 a year and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy a luxury boat for $590,000, close the health club, and travel the world in his boat for the rest of his life. Assume Paul has a remaining life of 25 years and earns 9 percent on his savings.

How much will Paul have in his savings on the day he starts his world tour assuming he has already paid for his boat? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Account value at retirement   

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

Annual withdrawal

Answer 1

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