Topics

Common cases

% increase

Example What is $80 with 10% increase?
Enter 80 + 10 %
Result 88

Other examples in this category:

  • What is $80 increased by 10%?
  • What is $80 with 10% added?
  • What is $80 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 80 × 10 %
Result 8

Inclusive case

Earlier we saw $80 with 10% increase gives the result $88.
That is, 80 + 10% = 88.

If that 10% is a tax rate, we say $88 is inclusive of tax. Or simply, $88 is the inclusive amount.

Often we are given the inclusive amount and the tax rate and we need to calculate other amounts.

% amount

Given the inclusive amount of 88 and the tax rate is 10%, what is tax amount?

To recall earlier, we learned that 80 × 10% = 8, that is

Original amount × Rate % = % amount

The inclusive case is similar; we just need to indicate the amount is inclusive.

Amount (inclusive) × Rate % = % amount

We use inc to indicate the amount is inclusive.

inc  is usually accessed by pressing the shortcut ⇧ i and we can change this to i:

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

Inclusive Button

Enter 88 inc × 10 %
Result 8

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

Compounding cases

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 2000 × 10%^3
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

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.

Find the original amount

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

Find the unknown

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