How the Finance Calculator Works
Almost every savings plan has five parts: the amount you start with, the amount you add regularly, the yearly return, the time, and the goal. If you know four of them, you can find the fifth. That is the idea behind the time value of money. The Finance Calculator lets you pick which part to find and fill in the rest.
The five parts
- Starting amount: the money you have now.
- Deposit: what you add each period, such as each month.
- Yearly return: the growth you expect. Interest is added at the same rhythm as your deposits.
- Years: how long you save.
- Goal: the amount you want to have at the end.
The one equation
All five are linked by a single equation. With a rate i for each period and n periods:
goal = start x (1 + i)^n + deposit x ((1 + i)^n - 1) / i
The first part is what your starting amount grows to. The second is what all your deposits grow to. If you add money at the start of each period instead of the end, the second part is multiplied by (1 + i). If the return is 0%, nothing grows, and the deposits are simply added up.
The five questions
| You want to find | How it is found |
|---|---|
| What my savings will grow to | Put the numbers into the equation |
| How much I need to save each period | (goal - what the start grows to) / the growth factor of the deposits |
| How much I need to start with | (goal - what the deposits grow to) / (1 + i)^n |
| How long it will take | Solve for n with logarithms |
| What return I need | Trial and refinement, because there is no simple formula |
A worked example
You have $10,000 and add $400 a month. The return is 6% a year, compounded monthly. After 15 years, your savings grow to $140,868.42. You put in $82,000, and interest adds $58,868.42.
Now say your goal is $150,000 in 15 years. Each question gives a different answer:
| Question | Answer |
|---|---|
| How much do I need to save each month? | $431.40 (instead of $400) |
| How much do I need to start with? | $13,720.96 (instead of $10,000) |
| What return do I need? | 6.647% a year, which is 6.854% after compounding |
| How long will it take? | 15 years 9 months (189 deposits, ending at $151,009) |
For the last question, the calculator counts whole deposits, so it rounds up to the first deposit that reaches the goal.
Chart: the balance over the years
The first example, in thousands of dollars. The growth speeds up as the interest starts to earn interest:
Start ███ 10 Year 3 ████████ 28 Year 6 ██████████████ 49 Year 9 █████████████████████ 74 Year 12 ██████████████████████████████ 105 Year 15 ████████████████████████████████████████ 141
Tips
- Start early. A longer time helps more than a higher deposit.
- Try each question. Asking "how long" and "how much each month" for the same goal shows your choices.
- Be careful with the return. If you must earn a very high return to reach a goal, the plan is risky. Save more or wait longer instead.
- Pay attention to timing. Adding money at the start of each period gives it one more period of growth.
What this calculator does not include
- Taxes and fees, which lower your real return.
- Changes in your deposit or in the rate over time.
- The effect of inflation. Your goal will buy less in the future, so consider a larger goal.
- Loans. For borrowing, use a loan calculator, where you owe the money instead of saving it.
This tool gives an estimate for general information only. It is not financial or investment advice. Returns are not guaranteed.