% increase

Example What is $60 with 10% increase?
Enter 60 + 10 %
Result 66

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.


% decrease

Example What is $70 with 10% decrease?
Enter 70 10 %
Result 63

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.


% amount

Example What is 10% of $80?
Enter 10 % × 80
Result 8

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.


% amount

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)

We use inc to indicate the amount is inclusive.

inc  is not easy to find. Let’s make it easier.

Hold down the button “i” until the menu appears and choose “Inclusive of %”.

Inclusive Button

Tip:  The shortcut for inc  is now i

Enter 10 % × 88 inc
Result 8

You can also enter  10 % 88 inc  or  88 inc × 10 %


Original amount

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 inc 10 %
Result 80

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:

Compound Convention

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:

Compound Math

You can see the similarity:

Compound Syntax


Enter 2000 + 10% xy 3
Result 2662

You can press Y or ^ for xy
We will use ^ to illustrate.


Compounded amount

This is the interest amount from our example. It’s very similar to calculating % amount.

Enter 10%^3 × 2000
Result 662

Depreciation

Similar to % decrease, but in a compounded way.

Example:
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
Result 4698.056…

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?

Enter 2662 inc – 10%^3
Result 2000

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.

Our expression

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.

Monthly compounding expression

Remember
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