What is the compound interest formula?
If you’ve heard of saving and investing, you’ll have heard of the “power of compound interest!” But what is compound interest? How it works? Why is this important? And what is the compound interest formula? We will take a look.
What is compound interest?
People who already have money find it easier to get more of it just by letting their savings grow. That’s the power of compound interest.
If you lend money, the borrower will pay you back, plus fees. These fees are interest, and it’s usually a percentage of the money you loaned them.
If you lend me Â£ 100 at 10% interest, I’ll pay you back Â£ 110 – that’s the original Â£ 100, which we call principal, plus Â£ 10 interest. You could keep loaning me the same Â£ 100 and earn Â£ 10 every time. After ten loans you would have the original Â£ 100 plus Â£ 100 interest. This is how simple interest works.
Compound interest is more powerful. If, instead of lending me just Â£ 100 the second time around, you lend me the full Â£ 110 at the same interest rate, then I’ll pay you back Â£ 121 – that’s the principal of Â£ 110, plus Â£ 11 of interests. Next time around, you’ll get Â£ 133.10. If you keep reinvesting principal and interest, your money will grow exponentially. Let’s look at the numbers.
Principal (amount loaned) | 10% interest | Total reimbursed | Total profit | |
1 | Â£ 100.00 | Â£ 10.00 | Â£ 110.00 | ten% |
2 | Â£ 110.00 | Â£ 11.00 | Â£ 121.00 | 21% |
3 | Â£ 121.00 | Â£ 12.10 | Â£ 133.10 | 33.1% |
4 | Â£ 133.10 | Â£ 13.31 | Â£ 146.41 | 46.41% |
5 | Â£ 146.41 | Â£ 14.64 | Â£ 161.05 | 61.05% |
6 | Â£ 161.05 | Â£ 16.10 | Â£ 177.16 | 77.16% |
7 | Â£ 177.16 | Â£ 17.72 | Â£ 194.87 | 94.87% |
8 | Â£ 194.87 | Â£ 19.49 | Â£ 214.36 | 114.36% |
9 | Â£ 214.36 | Â£ 21.44 | Â£ 235.79 | 135.79% |
ten | Â£ 235.79 | Â£ 23.58 | Â£ 259.37 | 159.37% |
After re-loaning ten times, you will have earned almost 160% on top of your capital. After twenty-five times, you will have won almost 900%! That’s the power of compound interest: the more you reinvest your interest, the faster your investment grows.
How to calculate compound interest?
You can calculate it step by step or use an online calculator (try the Motley Fool Savings Calculator!), But it’s easy to calculate yourself. Better yet, it will help you understand how the compound interest formula works.
Above, every time we loaned money we would calculate the interest and then add it to the principal. We can do this all at once by multiplying the principal by (1 + interest rate). Let us call the principal “P” and the interest rate “r”. If we reinvest twice, we end up with:
P x (1 + r) x (1 + r)
We can write this more clearly as P (1 + r)^{2}
To generalize this formula:
- P is the main
- r is the interest rate
- n is the number of times we compound the interest in each period of time
- t is the number of periods.
This gives us the compound interest formula:
P (1 + r / n)^{nxt}
Let’s look at our original loan, when you loaned me Â£ 100 at 10% interest. If it’s compounded annually, and you’ve loaned it to me for 10 years. You would end up with:
100 x (1 + 0.1 / 1)^{(1 Ã— 10)} = 100 x 1.1^{ten} = Â£ 259.73
What if I paid the same interest rate, but compounded monthly rather than annually? If you lent it to me for the same 10 years, you would end up with:
100 x (1 + 0.1 / 12)^{(12 Ã— 10)} = 100 x (1 + 0.1 / 12)^{120} = Â£ 270.70
So, you see, understanding the compound interest formula helps you understand why you should check how often the interest is compounded rather than just the interest rate. By dialing monthly rather than annually, you earned an additional Â£ 11.
How to benefit from compound interest?
In reality, my friends don’t pay me interest when I lend them money – but my bank does! Compound interest makes your money grow in savings accounts, term deposits, and bonds. However, the same principles – and the same compound interest formula – apply to any investment if you reinvest your profits.
What’s the downside?
There’s always a downside, and compound interest is no different. It’s great if you’re the person earning the interest, but not if you’re the one paying it. Credit cards and loans can easily get out of hand if you don’t meet payments.
To avoid this, choose a 0% credit card to dodge the negative effects of compound interest.
To take with
The compound interest formula can help you understand what is happening to your money and why. If you keep reinvesting in a low-cost, high-interest account that compounds frequently, your wealth will increase. That’s the power of compound interest.
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