Interest

Suppose you have $100 to invest in a savings account. The bank offers two plans. Plan 1 pays you a fixed interest amount of $100 each day. Plan 2 pays you 5% compounded each day. Which do you pick?

To answer our question, plan 1 pays you $100 interest after the first day, an additional $100 interest the second day, and an additional $100 each day you maintain the account. That sounds really attractive. If you deposited the $100 on Monday, your total on Friday would be $500!!!

Plan 2 doesn't sound as attractive. It earns $10% interest on the current balance each day. On the fist day, it would earn only $10 in interest, far below the amount you would have received under plan 1. By Friday, the account would only total $146.41. Obviously, plan 1 is better, right? The answer is not necessarily.

When evaluating the plans, it is important to consider not just the rate, but also the expected time period. On the 38th day after deposit, the balance in plan 1 would be $3,900. The balance in plan 2 would be only $3,740.43. But starting the 39th day, plan 2 becomes the better choice. Plan 1 would add $100 in interest bring the total to $4,000. Plan 2 would add $374.04 in interest bringing the total to $4,114.48.

So which plan would you select? If you planned to keep the funds in the account for over 39 days, you ought to pick plan 2.

The example here is highly exaggerated, it is doubtful you would find a bank offering an account earning 10% compounded daily.

While compound interest on your savings works to your advantage, compound interest on your loans and credit cards will work against you.

Check to see the math behind these plans

The new balance for each plan is the current balance + interest.
Plan 1 daily interest = fixed at $100.
Plan 1 new balance after N days = $100 + N × $100
  e.g. new balance after 5 day is $100 + 5 × $100 = $600

Plan 2 daily interest = current balance × 0.10
Plan 2 new balance after N days = $100 ( 1 + .01) ** N
      e.g. new balance after 5 days is $500 ( 1 + 1.01) ** N

DAY		PLAN1		PLAN2
0		$100.00		$100.00
1		$200.00		$110.00
2		$300.00		$121.00
3		$400.00		$133.10
4		$500.00		$146.41
5		$600.00		$161.05
6		$700.00		$177.16
7		$800.00		$194.87
8		$900.00		$214.36
9		$1,000.00		$235.79
10		$1,100.00		$259.37
11		$1,200.00		$285.31
12		$1,300.00		$313.84
13		$1,400.00		$345.23
14		$1,500.00		$379.75
15		$1,600.00		$417.72
16		$1,700.00		$459.50
17		$1,800.00		$505.45
18		$1,900.00		$555.99
19		$2,000.00		$611.59
20		$2,100.00		$672.75
21		$2,200.00		$740.02
22		$2,300.00		$814.03
23		$2,400.00		$895.43
24		$2,500.00		$984.97
25		$2,600.00		$1,083.47
26		$2,700.00		$1,191.82
27		$2,800.00		$1,311.00
28		$2,900.00		$1,442.10
29		$3,000.00		$1,586.31
30		$3,100.00		$1,744.94
DAY		PLAN1		PLAN2
31		$100.00		$1,919.43
32		$200.00		$2,111.38
33		$300.00		$2,322.52
34		$400.00		$2,554.77
35		$500.00		$2,810.24
36		$600.00		$3,091.27
37		$700.00		$3,400.39
38		$800.00		$3,740.43
39		$900.00		$4,114.48
40		$1,000.00		$4,525.93
41		$1,100.00		$4,978.52
42		$1,200.00		$5,476.37
43		$1,300.00		$6,024.01
44		$1,400.00		$6,626.41
45		$1,500.00		$7,289.05
46		$1,600.00		$8,017.95
47		$1,700.00		$8,819.75
48		$1,800.00		$9,701.72
49		$1,900.00		$10,671.90
50		$2,000.00		$11,739.09
51		$2,100.00		$12,912.99
52		$2,200.00		$14,204.29
53		$2,300.00		$15,624.72
54		$2,400.00		$17,187.19
55		$2,500.00		$18,905.91
56		$2,600.00		$20,796.51
57		$2,700.00		$22,876.16
58		$2,800.00		$25,163.77
59		$2,900.00		$27,680.15
60		$3,000.00		$30,448.16
61		$3,100.00		$33,492.98
DAY		PLAN1		PLAN2
62		$100.00		$36,842.28
63		$200.00		$40,526.51
64		$300.00		$44,579.16