Question

different cash flow. given the following cash flow at the end of each year, what is the future value of this cash flow at 3%, 9%, and 18% interest rates at the end of year 7?

year 1.                     $15,000
year 2.                     $20,000
year 3.                     $29,000
year4 through 6.    $0
year 7.                     $130,000

Answer 1

Calculation of future value of different cash flows:

Future value = Present value (1+r)ⁿ

Where, r is rate of interest and n is number of year.

1) For cash flow of $15,000:

Given cash flow is at the end of year 1, it means that this cash flow is at the beginning of year 2. So, for calculating future value n will be 0 for year 1, 1 for year 2, 2 for year 3, 3 for year 4, 4 for year 5, 5 for year 6, 6 for year 7. Hence discounting factor of year 1 shall be taken for year 2, of year 2 for year 3 and so on.

Accordingly future value shall be,

Year	Particulars	Rate 3%		Rate 9%		Rate 18%
		Discounting Factor 1/(1+r)n	Discounted amount	Discounting Factor	Discounted amount	Discounting Factor	Discounted amount
1	Cash flow $15,000	1/(1+0.03)2=0.9426	14139	1/(1+0.09)2=0.8417	12625.5	1/(1+0.18)2=0.7182	10773
2	Cash flow $15,000	1/(1+0.03)3=0.9151	13726.5	1/(1+0.09)3=0.7722	11583	1/(1+0.18)3=0.6086	9129
3	Cash flow $15,000	1/(1+0.03)4=0.8885	13327.5	1/(1+0.09)4=0.7084	10626	1/(1+0.18)4=0.5158	7737
4	Cash flow $15,000	1/(1+0.03)5=0.8626	12939	1/(1+0.09)5=0.6499	9748.5	1/(1+0.18)5=0.4371	6556.5
5	Cash flow $15,000	1/(1+0.03)6=0.8375	12562.5	1/(1+0.09)6=0.5963	8944.5	1/(1+0.18)6=0.3704	5556
6	Cash flow $15,000	1/(1+0.03)7=0.8131	12196.5	1/(1+0.09)7=0.5470	8205	1/(1+0.18)7=0.3139	4708.5
7	Cash flow $15,000	1/(1+0.03)8=0.7894	11841	1/(1+0.09)8=0.5019	7528.5	1/(1+0.18)8=0.2660	3990
	Total		90732		69261		48450

2) For cash flow of $20,000 at the end of year 2:

At the end of year 2 means at the beginning of year 3. So discounting factors will change. For year 2, year 3 discounting factor will be there and so on.

Year	Particulars	Rate 3%		Rate 9%		Rate 18%
		Discounting Factor 1/(1+r)n	Discounted amount	Discounting Factor	Discounted amount	Discounting Factor	Discounted amount
2	Cash flow $20,000	1/(1+0.03)3=0.9151	18302	1/(1+0.09)3=0.7722	15444	1/(1+0.18)3=0.6086	12172
3	Cash flow $20,000	1/(1+0.03)4=0.8885	17770	1/(1+0.09)4=0.7084	14168	1/(1+0.18)4=0.5158	10316
4	Cash flow $20,000	1/(1+0.03)5=0.8626	17252	1/(1+0.09)5=0.6499	12998	1/(1+0.18)5=0.4371	8742
5	Cash flow $20,000	1/(1+0.03)6=0.8375	16750	1/(1+0.09)6=0.5963	11926	1/(1+0.18)6=0.3704	7408
6	Cash flow $20,000	1/(1+0.03)7=0.8131	16262	1/(1+0.09)7=0.5470	10940	1/(1+0.18)7=0.3139	6278
7	Cash flow $20,000	1/(1+0.03)8=0.7894	15788	1/(1+0.09)8=0.5019	10038	1/(1+0.18)8=0.2660	5320
	Total		102124		75514		50236

3) For cash flow of $29,000 at the end of year 3:

At the end of year 3 means at the beginning of year 4, so discounting factor will be for year 3 it will be of year 4.

Year	Particulars	Rate 3%		Rate 9%		Rate 18%
		Discounting Factor 1/(1+r)n	Discounted amount	Discounting Factor	Discounted amount	Discounting Factor	Discounted amount
3	$29,000	1/(1+0.03)4=0.8885	25766.5	1/(1+0.09)4=0.7084	20543.6	1/(1+0.18)4=0.5158	14958.2
4	$29,000	1/(1+0.03)5=0.8626	25015.4	1/(1+0.09)5=0.6499	18847.1	1/(1+0.18)5=0.4371	12675.9
5	$29,000	1/(1+0.03)6=0.8375	24287.5	1/(1+0.09)6=0.5963	17292.7	1/(1+0.18)6=0.3704	10741.6
6	$29,000	1/(1+0.03)7=0.8131	23579.9	1/(1+0.09)7=0.5470	15863	1/(1+0.18)7=0.3139	9103.1
7	$29,000	1/(1+0.03)8=0.7894	22892.6	1/(1+0.09)8=0.5019	14555.1	1/(1+0.18)8=0.2660	7714
	Total		121541.9		87101.5		55192.8

4) For year 4-6 cash flow is $0

For cash flow of $0, anything that will be multiplied will be zero only. Therefore, future value for year 4-6 is $0.

5) For year 7 cash flow is $1,30,000:

Year	Particulars	Rate 3%		Rate 9%		Rate 18%
		Discounting Factor 1/(1+r)n	Discounted amount	Discounting Factor	Discounted amount	Discounting Factor	Discounted amount
7	Cash flow $1,30,000	1/(1+0.03)8=0.7894	102623.2	1/(1+0.09)8=0.5019	65242.62	1/(1+0.18)8=0.2660	34584.96
	Total		102623.2		65242.62		34584.96