Savings & Deposit Calculator, Compound Interest

About Savings & Deposit Calculator, Compound Interest

This calculator has two modes. The Savings mode follows how Korean banks price their products: a lump-sum time deposit (예금) or a monthly installment savings plan (적금), with simple or monthly-compounded interest, before and after Korea's 15.4% interest income tax, plus a reverse calculation from a target payout. The Compound interest mode is for long-horizon planning: a starting balance plus optional monthly or yearly contributions, compounded annually, semiannually, quarterly, monthly or daily, with a year-by-year table and an optional inflation adjustment.

Korean amounts and tax are the default, but the arithmetic is universal. If you live elsewhere, switch tax off and apply your own country's rate; the sections below show how that works in the US, the UK, Japan and Spain without pretending those rules are built into the tool.

Why an installment plan pays about half its headline rate

Put ₩1,000,000 a month into a 12-month plan advertised at 4%. The first deposit earns interest for 12 months; the last earns it for one. Korean banks compute simple interest on each deposit for the months it actually sat there, so interest is 1,000,000 × (0.04 ÷ 12) × (12 + 11 + … + 1) = 1,000,000 × 0.003333 × 78 = ₩260,000, not the ₩480,000 many people expect on ₩12,000,000 deposited.

The average deposit stays (n + 1) / 2 months, 6.5 months in a 12-month plan, so the return on everything you paid in is 4% × 13/24 ≈ 2.17%. After 15.4% tax that is ₩219,960, or 1.83%. The ratio (n + 1) / 2n stays near one half for any term; 24 months gives 25/48, about 52%.

The same logic applies to any regular saving plan anywhere: a UK regular saver at 7% or a US automatic monthly transfer into a savings account behaves the same way. When you compare a 7% regular saver against a 4% easy-access account, the regular saver's effective return over its first year is closer to 3.8% on the money you put in. It still wins if you had no lump sum to begin with; it loses if you did.

Simple versus monthly compounding over short terms

₩10,000,000 at 4% for one year earns ₩400,000 simple and ₩407,415 compounded monthly, a gap of ₩7,415. Over three years it is ₩1,200,000 versus ₩1,272,719. For the 12-month installment plan above, compounding moves interest from ₩260,000 to ₩263,204.

On products lasting one to three years, a tenth of a percentage point in rate and the early-withdrawal terms matter more than whether interest compounds. In the US and UK, banks quote APY or AER precisely so that you can compare accounts with different compounding on one number.

Tax on interest: Korea and some comparisons

Korea withholds 14% national income tax on interest (Income Tax Act Article 129) plus local income tax at 10% of that, 1.4%, for 15.4% in total. The bank deducts it at payment. If one person's combined interest and dividends exceed ₩20 million in a year, the excess is added to other income and taxed at progressive rates (Article 14), so 15.4% is not always the end of it. Tax-free products can be modeled by switching tax off.

Japan withholds 20.315% on bank interest: 15.315% national income tax including the reconstruction surtax, plus 5% local inhabitant tax. It is final withholding (源泉分離課税), so the interest is not reported on a tax return. Spain withholds 19% on account and deposit interest as an advance on income tax; the final rate in the savings base runs from 19% to 30% depending on the amount. In the US interest is ordinary income taxed at your marginal rate, and in the UK a Personal Savings Allowance applies before tax; neither is a flat rate, so enter an estimated after-tax rate in the Compound mode instead.

Compound mode: contributions and inflation dominate

The Compound mode converts the nominal rate to its effective annual rate (1 + r/n)^n for the chosen frequency, spreads that across months, and adds contributions before or after each month's interest. At 6%, the effective annual rates are 6% annual, 6.168% monthly and 6.183% daily; the jump from monthly to daily is trivial.

What really moves long-run results is how much you keep adding. ₩10,000,000 at 6% compounded monthly grows to about ₩33.1 million in 20 years on its own. Add ₩500,000 at the end of every month and it reaches about ₩264.1 million, of which ₩130 million is your own money. With 2.5% inflation, that ₩264.1 million is worth about ₩161.2 million in today's money. The same proportions hold in dollars or euros, since the math does not depend on currency.

This mode does not deduct tax. In a taxable account, try entering the after-tax rate, for example 6% × (1 − 0.154) ≈ 5.08% for Korea.

How accurate is the rule of 72?

Doubling time is roughly 72 divided by the annual rate. Compared with the exact figure for annual compounding, ln 2 / ln(1 + r), it is nearly exact from 6% to 10% and drifts at the ends:

• 2%: rule of 72 says 36 years; exact 35.0
• 4%: 18 vs 17.7
• 8%: 9 vs 9.01
• 12%: 6 vs 6.12
• 24%: 3 vs 3.22

Worked examples

How to use it

1. Pick Savings mode for a bank deposit or installment plan, or Compound mode for long-term planning.
2. Enter rate, term and amount (lump sum, monthly payment, or starting balance and contributions).
3. Choose taxed or tax-free; with the reverse (target) option on, enter the payout you want and read the required amount.

Frequently asked questions