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Finance

Compound interest, interest, loan payments, inflation and rate of return.

In finance, time works just as hard as the interest rate: interest added to the principal starts earning alongside it, and a loan payment spreads that relationship over several hundred months. The calculators show not only the result, but also how much of the total is interest.

Calculators

6

Compound interest

K = k · (1 + r / n)ⁿᵗ
%
Final value16,470.09
  • Total interest6,470.09
  • Increase64.70%
  • Effective annual rate5.12%
  • Principal doubles after13.89 years

Simple interest

O = k · r / 100 · t
%
Interest1,500.00
  • Total after the period11,500.00
  • Monthly41.67
  • After 19 % tax1,215.00

Annuity loan payment

R = K · i / (1 − (1 + i)⁻ⁿ)
%
Monthly payment2,158.77
  • Number of payments300
  • Total repaid647,629.82
  • Interest cost347,629.82
  • Interest in the first payment1,800.00

Regular saving

FV = w · ((1 + i)ⁿ − 1) / i
%
Capital accumulated77,641.14
  • Total deposits60,000.00
  • Interest earned17,641.14
  • Number of deposits120

Inflation: purchasing power

real = amount / (1 + i)ᵗ
%
Real value after 10 years708.92
  • Value lost291.08
  • Loss of purchasing power29.11%
  • Amount of equal purchasing power1,410.60

Rate of return and CAGR

CAGR = (b / a)^(1 / t) − 1
Annualized (CAGR)10.53%
  • Total return (ROI)65.00%
  • Profit6,500.00
  • Multiplier1.65

Tables and cheat sheets

2

The rule of 72 — how many years until the principal doubles

the 72 / r approximation next to the exact result
Annual rate72 / rExactAfter 10 years it grows by
1 %7269.6610.5%
2 %363521.9%
3 %2423.4534.4%
4 %1817.6748.0%
5 %14.414.2162.9%
6 %1211.979.1%
7 %10.310.2496.7%
8 %99.01115.9%
9 %88.04136.7%
10 %7.27.27159.4%
11 %6.56.64183.9%
12 %66.12210.6%

Growth of a principal of 10,000 with annual compounding

compound interest, with no extra deposits and no tax
Years3 %5 %8 %12 %
110,30010,50010,80011,200
210,60911,02511,66412,544
310,92711,57612,59714,049
511,59312,76314,69317,623
1013,43916,28921,58931,058
1515,58020,78931,72254,736
2018,06126,53346,61096,463
2520,93833,86468,485170,001
3024,27343,219100,627299,599

Worked examples with full solutions

2

A deposit compounded monthly

$10,000 at 5 % a year, compounded monthly, for 10 years. How much will be in the account?

  1. Rate per period5 % / 12 = 0,4167 % = 0,0041667
  2. Number of periods12 · 10 = 120
  3. The compound interest formulaK = 10 000 · (1 + 0,0041667)¹²⁰
  4. ResultK = 10,000 · 1.647009 = $16,470.09
  5. Interest and capital gains tax$6,470.09 of interest; $5,240.77 is left after 19 % tax

Answer: The account holds $16,470.09, or $15,240.77 after capital gains tax.

Loan payment and total cost

$300,000 over 25 years at 7.2 % — what is the annuity payment?

  1. Monthly rate and number of paymentsi = 7,2 % / 12 = 0,006 ; n = 300
  2. The annuity payment formulaR = K · i / (1 − (1 + i)⁻ⁿ)
  3. SubstituteR = 300,000 · 0.006 / (1 − 1.006⁻³⁰⁰) = 1,800 / 0.83381 = $2,158.77
  4. Total repaid2,158.77 · 300 = $647,629.82, of which $347,629.82 is interest

Answer: The payment is about $2,158.77, and the interest over 25 years comes to about $347,630.

See also

PercentagesPercentage of a number, percentage change, increases and discounts, percentage points.VAT and tradeNet, gross, margin, markup, discounts and unit price.Fractions and ratiosConverting fractions to percentages, fraction arithmetic, the rule of three and scale.