discount - the amount by which the market price of a bond is lower than its principal amount due at maturity

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bul

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay?
[U]Calculate Discount Percent:[/U]
If the teachers got a 24% discount, that means they paid:
100% - 24% = 76%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent)
[U]Calculate discount price:[/U]
Discount Price = Full Price * (Discount Percent)
Discount Price = 5230 * 0.76
Discount Price = 3974.80
Price per teacher = Discount Price / Number of Teachers
Price per teacher = 3974.80 / 20
Price per teacher = [B]$198.74[/B]

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax
Figure out the total cost before the discount:
Total Cost before discount = Cases * Price per case
Total Cost before discount = 3 cases * $21.95 per case
Total Cost before discount = $65.85
Now, find the discounted value of the apples:
Discounted Apple Price = Total Cost before discount * (1 - discount percent)
Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2
Discounted ApplesPrice = $65.85 * 0.8
Discounted ApplesPrice = $52.68
Now, apply the sales tax to this discounted value to get the total bill:
Total Bill = Discounted Apple Price * (1 + tax rate)
Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075
Total Bill = $52.68 * 1.075
Total Bill = [B]$56.63[/B]

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percen

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given?
Let the second discount be d. We're given:
480 * (1 - 0.3)(1 - d) = 285.60
480(0.7)(1 - d) = 285.60
336(1 - d) = 285.60
336 - 336d = 285.60
[URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get:
d = [B]0.15 or 15%[/B]

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how mu

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how much will it cost after tax?
[U]Calculate percent off first:[/U]
10% off means 90% off the price
$18.50 * (1 - 0.1)
$18.50 * (0.9) = 16.65
[U]Now, add 7% sales tax to the discounted price[/U]
Price after sales tax = Discounted Price * 1.07
Price after sales tax = 16.65(1.07)
[B]Price after sales tax = 17.82[/B]

A book is discounted 45%. If the original price is $40, what is the new price?

A book is discounted 45%. If the original price is $40, what is the new price?
45% discount means we pay 100% - 45% = 55%
40 * 55% = [B]22[/B]

a book which was marked at $84 was sold for $75.60 .calculate the percent discount

a book which was marked at $84 was sold for $75.60 .calculate the percent discount
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=84&m=&p2=+75.60&pl=Calculate']markdown calculator[/URL], we get:
[B]10% markdown/percent discount[/B]

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this shelf take an additional 25% off."
Leta picked out books from the discount shelf that had a regular price of $100. How much did Leta pay for the discounted books?
100 with 50% discount is $40
$50 with a 25% discount is $12.50 off
$50 - $12.50 = [B]$37.50[/B]

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on t

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on the camera
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=450&m=&p2=+315&pl=Calculate']markdown calculator[/URL], we get:
[B]-30%[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the mon

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this?
to start, we have:
[LIST]
[*]Let the salesman's monthly sales be s.
[*]With a 10% discount as a decimal of 0.1
[*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality
[*]We want 10% times s + 800 per month is greater than or equal to 3200
[/LIST]
We want the inequality:
0.1s + 800 >= 3200
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get:
[B]s >= 24000[/B]

A clothing store buys shirts for n dollars and then marks them up 50%. To reward their employees, th

A clothing store buys shirts for [I]n[/I] dollars and then marks them up 50%. To reward their employees, the store gives a 50% discount to all employees. How much does an employee pay for a shirt?
50% = 0.5
Markup cost = (1 + 0.5)n
Markup cost = 1.5n
50% discount:
1.5n/2 = [B]0.75n[/B]

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off of the discounted priced. How much does the coat cost now?
Calculate discounted price:
Discounted Price = Full Price * (1 - Discount Percentage)
Discounted Price = 100 * (1 - 0.20) <-- Since 20% = 0.2
Discounted Price = 100 * (0.80)
Discounted Price = 80
Now calculate marked down price off the discount price:
Markdown Price = Discount Price * (1 - Markdown Percentage)
Markdown Price = 80 * (1 - 0.30) <-- Since 30% = 0.3
Markdown Price = 80 * (0.70)
Markdown Price = [B]56[/B]

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold for $5.76 apiece. What is the mark-up, as a percentage?
Using our [URL='https://www.mathcelebrity.com/markup.php?p1=3.80&m=&p2=5.76&pl=Calculate']markup calculator[/URL], we get:
[B]51.58% markup[/B]

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost of the guitar including tax?
Discount Amount = 0.2n
Total paid after discount = n - 0.2n = 0.8n
Tax amount:
0.8n * 0.08 = 0.064n
After tax amount:
0.8n + 0.64n = [B]0.864n[/B]

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the fin

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the final cost
[U]Calculate discounted price:[/U]
Discounted price = Full price * (100% - discount percent)
Discounted price = 129.99 * (100% - 20%)
Discounted price = 129.99 * 80%
Since 80% = 0.8, we have:
Discounted price = 129.99 * 0.8
Discounted price = 103.99
[U]Calculate after tax cost:[/U]
Tax Rate = Tax percent/100
Tax Rate = 8/100
Tax Rate = 0.08
After Tax cost = Discounted price * (1 + Tax rate)
After Tax cost = 103.99 * (1 + 0.08)
After Tax cost = 103.99 * 1.08
After Tax cost = [B]112.31[/B]

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale pri

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale price be for water skis which regularly sell for $248?
[U]Calculate Sale Price:[/U]
Sale Price = Full Price * (1 - sale discount)
Sale Price = 248 * (1 - 0.2) <-- since 20% is 0.2
Sale Price = 248 * (0.8)
Sale Price = [B]198.40[/B]

A store is offering a 11% discount on all items. Write an equation relating the final price

A store is offering a 11% discount on all items. Write an equation relating the final price
11% discount means we pay 100% - 11% = 89% of the full price. Since 89% as a decimal is 0.89. With a final price f and an original price p, we have:
[B]F = 0.89p[/B]

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an item to its list price L
If we give a discount of 15%, then we pay 100% - 15% = 85% of the list price. 85% as a decimal is 0.85, So we have:
L = 0.85S

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L.
18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price:
S = L(1 - 0.18)
[B]S = 0.82L[/B]

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales ta

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales tax. How much will the toaster oven cost?
[U]Calculate discounted price:[/U]
Discounted Price = Full Price * (1 - Discount Percent)
Since 30% = 0.3, we have
Discounted Price = 35 * (1 - 0.3)
Discounted Price = 35 * 0.7
Discounted Price = 24.5
Calculate after-tax amount:
After-tax amount = Discounted Price * (1 + Tax Percent)
Since 8% = 0.08, we have
Discounted Price = 24.5 * (1 + 0.08)
Discounted Price = 24.5 * 1.08
Discounted Price = [B]26.46[/B]

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is th

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax?
Find the discounted price: 15% off of 192.94
Discounted Price = 192.94 * (1 - 0.15) <-- 15% as a decimal is 0.15, and 1 is 100%, so we subtract to get 85% of the original price
Discounted Price =192.94(0.85)
Discounted Price = $164
Now, add in the sales tax of 6% to the Discounted Price
Price after sales tax = Discounted Price * 1.06
Price after sales tax = $164 * 1.06
[B]Price after sales tax = $173.84[/B]

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was $18,100, find the discount and the new price.
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=&m=+6&p2=++18100&pl=Calculate']discount calculator[/URL], we get:
[B]Discount = $1,086
New Price = $17,014[/B]

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was 18,400, find the discount and the new price.
First, find the discount amount:
Discount Amount = 6% * 18,400 = [B]1,104
[/B]
[U]Calculate discounted price:[/U]
Discounted Price = Full Price - Discount Amount
Discounted Price = 18,400 - 1,104
Discounted Price = 18,400 - 1,104 = [B]17,296[/B]

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a $53 discount her discounted bill at the end of the year was 463 what is her monthly fee
Her full annual bill is found by adding the discounted annual bill to the discount amount:
Full annual bill = Discounted annual bill + discount amount
Full annual bill = 463 + 53
Full annual bill = 516
Her monthly gym membership is found by the following calculation:
Monthly Gym Membership = Full Annual Bill / 12
Monthly Gym Membership = 516 / 12
Monthly Gym Membership = [B]$43[/B]

Bond Price Formulas

Free Bond Price Formulas Calculator - Given a face value, coupon percent, yield percent, term, and redemption value, this calculates the price of a bond using the four price formulas for bonds

1) Basic

2) Premium/Discount

3) Base

4) Makeham

1) Basic

2) Premium/Discount

3) Base

4) Makeham

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum d

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax
Let the original price be p.
p
Apply 25% discount first, which is the same as subtracting 0.25:
p(1 - 0.25)
Subtract 30 for in store buck
p(1 - 0.25) - 30
The phrase [I]no more than[/I] means an inequality using less than or equal to:
p(1 - 0.25) - 30 <= 60
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get:
[B]p <= 120[/B]

Chain Discounts and Net Cost Price and Net Cost Equivalent

Free Chain Discounts and Net Cost Price and Net Cost Equivalent Calculator - Given a chain discount and an original price, this calculates the total discount and net cost price.

Dividend Discount Model

Free Dividend Discount Model Calculator - This calculator determines the present value of dividends using the Dividend Discount Model.

If the original price of an item was $30.00 and Joan only paid $24.00 for it, what percentage discou

If the original price of an item was $30.00 and Joan only paid $24.00 for it, what percentage discount did Joan receive on her purchase?
She received 6 dollars off of a 30 dollar purchase, so we have 6/30 = 1/5 = 0.2 = [B]20%[/B]

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discou

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat?
Calculate discounted cost:
Discounted cost = Full Cost - Coupon
Discounted cost = 52 - 7
Discounted cost = 45
Since price equals rate * hours (h), and we want the inequality (less than) we have:
7h < 52
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7h%3C52&pl=Show+Interval+Notation']inequality calculator,[/URL] we see that:
[B]h < 7.42[/B]

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity pay

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent?
This is an annuity due, since the first payment is made on the date of purchase.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to m

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one?
Let the total bill be b. We have:
0.15b > 21 <-- Since 15% is 0.15
Using our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=0.15b%3E21&pl=Show+Interval+Notation']inequality calculator[/URL], we get [B]b>140[/B].
So any bill greater than $140 will make the 15% off option the best one, since the discount will be higher than $21.

Manuel can pay for his car insurance on a monthly basis, but if he pays an entire year's insurance i

Manuel can pay for his car insurance on a monthly basis, but if he pays an entire year's insurance in advance, he'll receive a $40 discount. His discounted bill for the year would then be $632. What is the monthly fee for his insurance?
His full bill F, is denoted as:
F - 40 = 632
[URL='https://www.mathcelebrity.com/1unk.php?num=f-40%3D632&pl=Solve']If we add 40 to each side[/URL], we get:
F = [B]$672[/B]

Mary paid 1.97 for toothpaste and a bar of soap using a discount coupon if the toothpaste cost 1.29

Mary paid 1.97 for toothpaste and a bar of soap using a discount coupon if the toothpaste cost 1.29 and the song cost 83 cents. What is the value of the discount coupon?
Find the full price package:
1.29 + 0.83 = 2.12
The value of the discount coupon is the money off, so:
2.12 - 1.97 = [B]0.15[/B]

Method of Equated Time-Exact Method-Macaulay Duration-Volatility

Free Method of Equated Time-Exact Method-Macaulay Duration-Volatility Calculator - Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Modified Payback Period

Free Modified Payback Period Calculator - Given a set of cash inflows, outflows, and a discount rate, this calculates the modified payback period.

Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_{t} at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.9

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza?
[U]Determine additional amount the pizzas would have cost without the coupon[/U]
6 pizzas * 3 per pizza = 18
[U]Add 18 to our discount price of 38.94[/U]
Full price for 6 large pizzas = 38.94 + 18
Full price for 6 large pizzas = 56.94
Let x = full price per pizza before the discount. Set up our equation:
6x = 56.94
Divide each side by 6
[B]x = $9.49[/B]

Simple Discount and Compound Discount

Free Simple Discount and Compound Discount Calculator - Given a principal value, interest rate, and time, this calculates the Accumulated Value using Simple Discount and Compound Discount

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The original price of a computer was $895.00. Eleanor had a 25% off coupon which she was able to us

The original price of a computer was $895.00. Eleanor had a 25% off coupon which she was able to use to make the purchase. If sales tax of 6.5% was added after the discount was taken, how much did Eleanor pay altogether for the computer?
First, apply the discount:
$895 * 25% = $223.75
$895 - $223.75 = $671.25
Now, apply sales tax of 6.5% to this discount price of $671.25
$671.25 * 1.065 = [B]$714.88[/B]

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal?
Minutes Rachel talks = m
Current plan cost = 0.12m
New plan cost = 0.005m + 46
Set new plan equal to current plan:
0.005m + 46 = 0.12m
Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides
0.005m + 46 - 0.12m = 0.12m - 0.12m
[SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE]
-0.115m + 46 = 0
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 46 and 0. To do that, we subtract 46 from both sides
-0.115m + 46 - 46 = 0 - 46
[SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE]
-0.115m = -46
[SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE]
-0.115m/-0.115 = -46/-0.115
m = [B]400
She must talk over 400 minutes for the new plan to be a better deal
[URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The population of a town is currently 22,000. This represents an increase of 40% from the population

The population of a town is currently 22,000. This represents an increase of 40% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole number if necessary.
To get the population 5 years ago, we'd discount the current population of 22,000 by 40%. We can write a 40% discount as 1.4.
Population 5 years ago = 22,000/1.4
Population 5 years ago = 15,714.29
Rounding to the nearest whole number, we get [B]15,714[/B]

The regular price for a television is Q dollars. Each Saturday televisions are 20% off (The discount

The regular price for a television is Q dollars. Each Saturday televisions are 20% off (The discount is .2Q). What is the price of a television on Saturday in terms of Q?
Q = Regular Price
.2Q = Discount
Discounted Price = Q - .2Q = [B]0.8Q[/B]

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the shirt has been discounted?
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=19&m=&p2=++13.30&pl=Calculate']markdown calculator[/URL], we get a 30% markdown, or sale.

The sale price of an item that is discounted by 20% of its list price L

The sale price of an item that is discounted by 20% of its list price L
S = L - 20%/100 * L
S = L - 0.20L
[B]S = 0.8L[/B]

The sales price of a new compact disc player is $210 at a local discount store. At the store where t

The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase?
If Kyle bought the player, he has 243 - 210 = 33 left over.
Each cd is 11, so set up an equation to see how many CDs he bought:
11x = 33
Divide each side by 11
[B]x = 3[/B]

Unit Savings

Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.

Vendor Discount Effective Rate of Interest

Free Vendor Discount Effective Rate of Interest Calculator - Calculates the effective rate of interest earned from a vendor discount for a prepayment of a balance within a certain amount of days for a percentage discount

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat?
A few things to build this problem:
[LIST=1]
[*]Discount subtracts from our total
[*]Cost = Hourly rate * hours
[*]Less than means an inequality using the < sign
[/LIST]
Our inequality is:
8h - 7 < 41
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get:
h < [B]6[/B]

You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7.

You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7. How many bottles of olive oil can you buy?
A $5 discount gives you $16 + $5 = $21 of buying power.
With olive oil at $7 per bottle, we have $21/$7 = [B]3 bottles of olive oil[/B] you can purchase