# % 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

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 to indicate the amount is inclusive.

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

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

 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: \$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% xy 3 Result 2662

You can press Y or ^ for
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. Remember
For monthly compounding, use a monthly rate.
Likewise weekly compounding… weekly rate, etc.
Identify the compounding period, use a suitable rate.

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.