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If you invest $20,000 today, how much will you have after:

a. 7 years at a 5 percent annual return

b. 10 years at a 7 percent annual return

Answer 1

Solution as below:

Year	Amount at start of the year	Annual interest	Accumulated balance at end of the year
Workings	Given for year 1, for other years it is accumulated balance of previous year	Amount at start of the year * 5% interest rate, say for year 1 it is 20,000 * 5% = 1000	Amount at the start of the year + Annual interest (sum of earlier two columns)
1	$                                   20,000.00	$                  1,000.00	$                                                             21,000.00
2	$                                   21,000.00	$                  1,050.00	$                                                             22,050.00
3	$                                   22,050.00	$                  1,102.50	$                                                             23,152.50
4	$                                   23,152.50	$                  1,157.63	$                                                             24,310.13
5	$                                   24,310.13	$                  1,215.51	$                                                             25,525.63
6	$                                   25,525.63	$                  1,276.28	$                                                             26,801.91
7	$                                   26,801.91	$                  1,340.10	$                                                             28,142.01

Answer for a is $28,142.01

For b:

Year	Amount at start of the year	Annual interest	Accumulated balance at end of the year
Workings	Given for year 1, for other years it is accumulated balance of previous year	Amount at start of the year * 7% interest rate, say for year 1 it is 20,000 * 7% = 1400	Amount at the start of the year + Annual interest (sum of earlier two columns)
1	$                                   20,000.00	$                     1,400.00	$                                                             21,400.00
2	$                                   21,400.00	$                     1,498.00	$                                                             22,898.00
3	$                                   22,898.00	$                     1,602.86	$                                                             24,500.86
4	$                                   24,500.86	$                     1,715.06	$                                                             26,215.92
5	$                                   26,215.92	$                     1,835.11	$                                                             28,051.03
6	$                                   28,051.03	$                     1,963.57	$                                                             30,014.61
7	$                                   30,014.61	$                     2,101.02	$                                                             32,115.63
8	$                                   32,115.63	$                     2,248.09	$                                                             34,363.72
9	$                                   34,363.72	$                     2,405.46	$                                                             36,769.18
10	$                                   36,769.18	$                     2,573.84	$                                                             39,343.03

Answer for b it is 39,343.03

The above can also be solved using FV formula in excel.