|Example||What is $60 with 10% increase?|
|Enter||60 + 10 %|
Other examples in this category:
- What is $60 increased by 10%?
- What is $60 with 10% added?
- What is $60 with 10% something*?
* where something can be tax, bonus, service charge etc.
|Example||What is $70 with 10% decrease?|
|Enter||70 – 10 %|
Other examples in this category:
- What is $70 with 10% off?
- What is $70 with 10% discount?
- What is $70 decreased** by 10%?
** Other similar words are reduced, lowered, cut etc.
|Example||What is 10% of $80?|
|Enter||10 % × 80|
Tip 1: You can leave out × and enter 10 % 80
Tip 2: You can also enter 80 × 10 %
From the last example, the original amount is $80.
10% of that is $8.
If this 10% is a tax rate, then the amount inclusive of tax is $80 + $8 = $88.
Often only the inclusive amount ($88) and the tax rate are known and we are here to calculate the other amounts.
In the simple case, the formulation is:
Rate % × Amount
The inclusive case is very similar; we just need to indicate the amount is inclusive.
Rate % × Amount (inclusive)
is not easy to find. Let’s make it easier.
Hold down the button “i” until the menu appears and choose “Inclusive of %”.
Tip: The shortcut foris now
|Enter||10 % × 88|
You can also enter 10 % 88or 88 × 10 %
One way to calculate the original amount is to use the formulation:
Amount (Inclusive) – Rate % = Original amount
You can think of it this way:
Amount inclusive of tax – tax = Original amount
Without further ado:
|Enter||88– 10 %|
Compound interest is a popular example of this.
It occurs in savings account, loans, and more.
Let’s use a savings account with 10% annual interest as an example. The initial deposit is $2000.
This means, in year 1, our saving will be:
2000 + 10% = 2200
In year 2, 10% of $2200 (year 1 saving) is added:
(2000 + 10%) + 10%
In year 3, you can see 10% is compounded 3 times:
((2000 + 10%) + 10%) + 10%
So year 7 means 7 compounding — it gets tediously long.
Of course there is an easier way.
A new convention in Magic Number:
You can read this as:
$2000 with 10% interest over 3 years.
Or better still:
2000 with 10% increase over 3 times.
‘3 times’ is the compounding frequency. If the interest is 10% monthly and the period is 3 months, the compounding frequency is still the same, and so is the calculation.
The actual math is:
You can see the similarity:
|Enter||2000 + 10%3|
You can press Y or ^ for
We will use ^ to illustrate.
This is the interest amount from our example. It’s very similar to calculating % amount.
|Enter||10%^3 × 2000|
Similar to % decrease, but in a compounded way.
The car costs $9000. It loses 15% of its value each year. How much the car is worth after 4 years?
|Enter||9000 – 15%^4|
Inclusive with compounding
Back to our savings account example.
The account’s balance, inclusive of 10% interest over 3 years is $2662. What is the initial deposit?
The shortcut for inclusive is ⇧i. If you are planning to use it a lot, scroll back for this tip.
Annual rate, monthly compounding
Often banks provide an annual rate while the interest is being added monthly.
2000 + 10% ^ 3
can be generalized as
Deposit + Annual rate % ^ compounding frequency
If the compounding is monthly, we need to use the monthly rate 10% ÷ 12. Compounding happens 12 times a year, and for 3 years the frequency will be 3 × 12 = 36.
For monthly compounding, use a monthly rate.
Likewise weekly compounding… weekly rate, etc.
Identify the compounding period, use a suitable rate.
You can learn more at Wikipedia.
Here’s an interesting way to find the original amount.
Let’s use x to represent the original amount.
|Example||If x + 25% = 90. What is x ?|
|Enter||? + 25% = 90|
|Result||? = 72|
|Example||If x – 20% = 96. What is x ?|
|Enter||? – 20% = 96|
|Result||? = 120|
Previously, we used ? to find the unknown original amount. ‘?’ is called ‘The Unknown’ — a bit like the unknown x in elementary algebra.
We can use it to find the unknown rates too.
|Example||If 120 – x % = 96. What is x ?|
|Enter||120 – ? % = 96|
|Result||? = 20|
This one involves % change:
|Example||125 Δ% x = 20%|
|Enter||125 Δ% ? = 20%|
|Result||? = 150|
You get Δ% by clicking F1 or F2. It is also under
Calculation > Extra Functions > Function Browser.
More details here.
You can use ? to solve other problems. Learn more