Interest and savings
Put money in and watch it grow. With compound interest you also earn interest on the interest — the table shows it year by year.
Your numbers
Your own interest rate — from the bank or the exercise.
More options: compounding, regular deposit
Paid in at the end of each period. Leave it at 0 for a starting amount only.
Answer
Final amount
13,439.16DKK
Total interest
3,439.16DKK
Paid in in total
10,000.00DKK
Doubled after
23.4 year
How to work it out
- 1K₀ · (1 + r)ⁿ = 10,000 · (1 + 0.03)^10 = 13,439.16The starting amount stays in for the whole period and earns compound interest.
- 2K = 13,439.16
The formula
K = K₀ · (1 + r)ⁿ
Compound interest: interest is added every period, and next period you also earn interest on the interest.
A = y · ((1 + r)ⁿ − 1) / r
Savings annuity: the value of n equal deposits y when the last one has just been paid in.
r = annual rate / periods per year · n = years · periods per year
effective rate = (1 + r)ᵐ − 1
If interest is added several times a year, you get a little more than the annual rate.
K = K₀ · (1 + r · n)
Simple interest: you only earn interest on the starting amount.
r is written as a decimal in the formula: 3 % = 0.03.
In depth: more numbers and “what if”
What if the interest rate is different?
| Interest per year | Final amount | Difference |
|---|---|---|
| 2 % | 12,189.94 DKK | -1,249.22 DKK |
| 2.5 % | 12,800.85 DKK | -638.32 DKK |
| 3 % | 13,439.16 DKK | — |
| 3.5 % | 14,105.99 DKK | 666.82 DKK |
| 4 % | 14,802.44 DKK | 1,363.28 DKK |
What if the money stays in longer?
| Number of years | Final amount | Total interest |
|---|---|---|
| 10 | 13,439.16 DKK | 3,439.16 DKK |
| 15 | 15,579.67 DKK | 5,579.67 DKK |
| 20 | 18,061.11 DKK | 8,061.11 DKK |
| 30 | 24,272.62 DKK | 14,272.62 DKK |
Year by year
| Year | Paid in that year | Interest that year | Amount |
|---|---|---|---|
| 0 | — | — | 10,000.00 |
| 1 | 0.00 | 300.00 | 10,300.00 |
| 2 | 0.00 | 309.00 | 10,609.00 |
| 3 | 0.00 | 318.27 | 10,927.27 |
| 4 | 0.00 | 327.82 | 11,255.09 |
| 5 | 0.00 | 337.65 | 11,592.74 |
| 6 | 0.00 | 347.78 | 11,940.52 |
| 7 | 0.00 | 358.22 | 12,298.74 |
| 8 | 0.00 | 368.96 | 12,667.70 |
| 9 | 0.00 | 380.03 | 13,047.73 |
| 10 | 0.00 | 391.43 | 13,439.16 |
More: Finance and money
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- Loans and savingsAnnuity and serial loans: payment, remaining debt and interest period by period.
- Energy and paybackWhen has an investment paid for itself? With your own saving and price.