Simple vs. compound interest

Two ways to grow money — and one of them barely matters

You put ₩1,000 in an account at 5%. After one year, you have ₩1,050. After two years, two questions split:

Simple interest: you earn 5% on the original ₩1,000 each year. Year 2: ₩1,000 + 5% = ₩1,050 of new interest plus the original ₩1,000 = ₩2,050. (Wait, that's the same number after one year. Let me redo.) Actually under simple interest, year 2 you earn another ₩50 (5% of the original ₩1,000), so total balance: ₩1,100. Year 3: another ₩50 → ₩1,150. Each year you add a flat ₩50.

Compound interest: you earn 5% on the current balance each year — including last year's interest. Year 2: 5% of ₩1,050 = ₩52.50, so balance: ₩1,102.50. Year 3: 5% of ₩1,102.50 = ₩55.13, so balance: ₩1,157.63. Each year the interest amount grows. Interest on interest.

The math

Two equations:

F V_{s im pl e} = P V \times (1 + r \times n)

F V_{co m p o u n d} = P V \times (1 + r)^{n}

The difference: simple interest is linear (multiply r by n and add 1). Compound interest is exponential (raise 1+r to the n power). After 1 year they give the exact same answer. After 30 years, they're worlds apart.

The picture: short term they look similar, long term they diverge wildly

₩1,000 at 5%, no withdrawals:

1 year — simple: ₩1,050 / compound: ₩1,050. Same.
5 years — simple: ₩1,250 / compound: ₩1,276. Tiny gap.
10 years — simple: ₩1,500 / compound: ₩1,629. Gap widening.
20 years — simple: ₩2,000 / compound: ₩2,653. Compound is 33% bigger.
30 years — simple: ₩2,500 / compound: ₩4,322. Compound is 73% bigger.
50 years — simple: ₩3,500 / compound: ₩11,467. Compound is 3.3x bigger.

This is why compound is the eighth wonder. The exponent eats the linear function alive over long enough horizons. By 30 years the compounded version is nearly double. By 50, it's more than 3x.

Which one does real life actually use?

Almost everything in modern finance is compound. Bank savings, mortgages, credit cards, bonds, stocks — all compound. Simple interest exists in a few specific contexts (some short-term loans, accrued interest on bonds between coupon dates), but if you're modeling growth or returns over multiple years, you assume compound.

The "miracle of compound interest" framing isn't marketing. It's just the exponent doing what exponents do over many years. Most long-term investing wisdom is downstream of this fact: start early (more years for the exponent), avoid withdrawing (interrupts compounding), keep costs low (1% taken away from compound is much more painful than 1% taken from simple).

The takeaway

Simple is linear, compound is exponential. They look the same after one year and dramatically different after 30. Modern finance defaults to compound. Whenever you see (1+r)^n, that's compound at work. Long horizons + compounding = where retirement money is supposed to come from. Long horizons + linear simple growth = retirement is harder than you'd think.