% increase, % decrease, % amount
Calculate from amount which is inclusive of %
Compound interest, depreciation etc.
- Find the original amount
- Find the unknown
|Example||What is $80 with 10% increase?|
|Enter||80 + 10 %|
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.
|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||80 × 10 %|
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.
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
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× 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||2000 × 10%^3|
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?
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