Question

What is the price of a security that will pay off $100 at the end of every year for the first 5 years ($100 year 1 through 5) and then every 5 years after that ($100 at the end of year 10, 15 …)? The annually compounded interest rate (EAR) is 10%. (HINT: put the cash payments on a time line).

Answer 1

We can calculate the present value in excel,

Yr	Amount	Discount factor 10% (1/(1+0.10)^t)	Amount
1	100	0.90909	90.909
2	100	0.82645	82.645
3	100	0.75131	75.131
4	100	0.68301	68.301
5	100	0.62092	62.092
10	100	0.38554	38.554
15	100	0.23939	23.939
20	100	0.14864	14.864
25	100	0.09230	9.230
30	100	0.05731	5.731
35	100	0.03558	3.558
40	100	0.02209	2.209
45	100	0.01372	1.372
50	100	0.00852	0.852
55	100	0.00529	0.529
60	100	0.00328	0.328
65	100	0.00204	0.204
70	100	0.00127	0.127
75	100	0.00079	0.079
80	100	0.00049	0.049
85	100	0.00030	0.030
90	100	0.00019	0.019
95	100	0.00012	0.012
100	100	0.00007	0.007
		Present Value	480.77

Hence the Present value is $480(approx).

If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.