Question

What is the equal payment series with the first payment in t=0 and the final payment in t=10, with a skipped payment at t=6, that is equivalent to a an increasing payment series where the first payment is $20,000 at t=2, and it is increasing by 8% each year with the final payment at t=10 (none skipped in the gradient)? Interest rate is 8%.

Answer 1

Rate of Interest = 8%

Present value is calculated as: [Cash Flow / (1 + Rate of Interest)^^Year]

Equal payment series:

Let annual equal payment be $X

Year	Cash Flow	Present Value
0	X	1.00X
1	X	0.93X
2	X	0.86X
3	X	0.79X
4	X	0.74X
5	X	0.68X
6	-	0.63X
7	X	0.58X
8	X	0.54X
9	X	0.50X
10	X	0.46X
		7.71X

Gradient payment series:

Payment increases by 8% every year

Year	Cash Flow	Present Value
0	-	-
1	-	-
2	20,000.00	17,146.78
3	21,600.00	17,146.78
4	23,328.00	17,146.78
5	25,194.24	17,146.78
6	27,209.78	17,146.78
7	29,386.56	17,146.78
8	31,737.49	17,146.78
9	34,276.49	17,146.78
10	37,018.60	17,146.78
		154320.99

To both of them to have equal value: 7.71X = 154,320.99

X = 20,015.69