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Simple vs compound interest on $1,000 at 5% for 50 years

$1,000 at 5% for 50 years becomes $3,500 with simple interest and $11,467 with compound interest, so compounding adds $7,967.

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The numbers for these inputs

YearSimpleCompoundDifference
1$1,050$1,050$0
2$1,100$1,103$3
3$1,150$1,158$8
4$1,200$1,216$16
5$1,250$1,276$26
6$1,300$1,340$40
7$1,350$1,407$57
8$1,400$1,477$77
9$1,450$1,551$101
10$1,500$1,629$129
11$1,550$1,710$160
12$1,600$1,796$196
13$1,650$1,886$236
14$1,700$1,980$280
15$1,750$2,079$329
16$1,800$2,183$383
17$1,850$2,292$442
18$1,900$2,407$507
19$1,950$2,527$577
20$2,000$2,653$653
21$2,050$2,786$736
22$2,100$2,925$825
23$2,150$3,072$922
24$2,200$3,225$1,025
25$2,250$3,386$1,136
26$2,300$3,556$1,256
27$2,350$3,733$1,383
28$2,400$3,920$1,520
29$2,450$4,116$1,666
30$2,500$4,322$1,822
31$2,550$4,538$1,988
32$2,600$4,765$2,165
33$2,650$5,003$2,353
34$2,700$5,253$2,553
35$2,750$5,516$2,766
36$2,800$5,792$2,992
37$2,850$6,081$3,231
38$2,900$6,385$3,485
39$2,950$6,705$3,755
40$3,000$7,040$4,040
41$3,050$7,392$4,342
42$3,100$7,762$4,662
43$3,150$8,150$5,000
44$3,200$8,557$5,357
45$3,250$8,985$5,735
46$3,300$9,434$6,134
47$3,350$9,906$6,556
48$3,400$10,401$7,001
49$3,450$10,921$7,471
50$3,500$11,467$7,967

How it works

Simple interest is calculated on the original amount only: balance = amount x (1 + rate x years). Every year earns the same interest.

Compound interest is calculated on the balance, which includes interest already earned: balance = amount x (1 + rate)^years. The gain grows each year, which is why the two lines pull apart over time.

Here the compound figure is compounded once a year. Monthly or daily compounding gives a slightly higher result at the same rate.

Common mistakes

  • Assuming the two are similar over short periods and long ones: after one year they are identical, after 30 years they are far apart.
  • Comparing a simple rate with a compound rate as if they were the same kind of number.
  • Forgetting that loans usually compound against you: the same effect works on debt.

Questions

Which is better, simple or compound interest?

For the person earning it, compound: it gives $7,967 more on these numbers. For a borrower, simple interest costs less.

What is the formula for each?

Simple: amount x (1 + rate x years). Compound: amount x (1 + rate)^years, compounded yearly in this calculator.

How much interest is earned in total on $1,000?

$2,500 with simple interest and $10,467 with compound interest.

Does the gap always grow?

Yes, as long as the rate is above zero. The difference is zero in year one and increases every year after, faster at higher rates.

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