Question

15. More on the time value of money Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organiz for divorce attorneys. The membership dues for the ADLA are $650 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $7,000 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, a great deal. Suppose that the appropriate annual interest rate is 5.9%. What is the minimum number of years that Lloyd must remain a member the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $650 in annual membership dues? (Note: Round your answer up to the nearest year.) 14 years 13 years 21 years 0 16 years

Answer 1

a.

Year (n)	Amount paid	DF = 1/(1+r)^n r=0.059	Present value = Amount paid * DF	Cumulative Presen vale
0	650	1.00	650.00	650.00
1	650	0.94	613.79	1,263.79
2	650	0.89	579.59	1,843.38
3	650	0.84	547.30	2,390.68
4	650	0.80	516.81	2,907.49
5	650	0.75	488.02	3,395.50
6	650	0.71	460.83	3,856.33
7	650	0.67	435.15	4,291.48
8	650	0.63	410.91	4,702.39
9	650	0.60	388.02	5,090.41
10	650	0.56	366.40	5,456.80
11	650	0.53	345.99	5,802.79
12	650	0.50	326.71	6,129.50
13	650	0.47	308.51	6,438.01
14	650	0.45	291.32	6,729.33
15	650	0.42	275.09	7,004.42
16	650	0.40	259.76	7,264.18
17	650	0.38	245.29	7,509.47
18	650	0.36	231.63	7,741.10
19	650	0.34	218.72	7,959.82
20	650	0.32	206.54	8,166.35
20	650	0.32	206.54	8,372.89
		NPV	8,372.89

here we have calculated the present value of the $650 paid every year for the next 21 years. the discounting factor is calculated by taking r= 5.9% and cumulative present value is calculated , by adding the present value of all the previous years and current year.

this is calculated to see in which year will the present value exceeds $7000. which happens in year 16, for whose the present value id $7264. so the answer is d, 16 years.

b.

Future value =Present Value * (1 + interest rate%)^n

n= tenor

here , Present value= $24

Tenor (n)= 392

interest rate= 4.5% or 0.045

so substituting all the values, FV= 24* (1+0.045)^392

FV= 74,78,20,036.24

So as per the calculations above , the answer is a.  $74,78,20,036.24