PRE1_SIMPLE INTEREST AND COMPOUND INTEREST Flashcards
What does each letter stands for:
I =
P =
r =
t =
F =
I = Interest Amount
P = Principal Amount
r = Rate of Interest per year in decimal; r = R/100
t = Time Periods involved
F = Final Amount
the person or institution that makes the funds available to those who need it.
Lender / Creditor
the person or institution that avails of the funds from the lender.
Borrower
a certain sum of money that the lender charges the borrower for the use of the funds.
Interest
is the sum of money borrowed or invested.
Principal (P)
The amount of money that you pay to borrow money or the amount of money that you earn on a deposit.
Interest (I):
The duration for which the money is borrowed/deposited.
Time (T):
is the rate charged by the lender or the rate of increase of the investment.
Rate of Interest (R)
Simple Interest Formula
I = Prt
Calculate time, solve for t
t = I / Pr
Calculate rate of interest in decimal, solve for r
r = I / Pt
Calculate Principal Amount, solve for P
P = I / rt
Calculate Interest, solve for I
I = Prt
Calculate Final Amount
(F) = P + I or F = P (1 + rt)
Note
- Base formula I = Prt, where P is the Principal amount of money to be invested at an Interest Rate r% per period for t Number of Time Periods. Where r is in decimal form; r=R/100. r and t are in the same units of time.
- If the loan is for less than 1 year, use the fraction of a year.
Rafael deposits P20,000 in a savings account that pays interest at the rate of 5% per year. How much is the interest and what will be the total amount after two years?
Given: P = P20,000 r = 5% or 0.05 t = 2
Solution: I = (20,000) (0.05) (2) = P2,000
F = P + I = 20,000 + 2,000 = P22,000
The interest is P2,000. The total amount of Rafael’s money after 2 years is P22,000.
At what annual interest rate is P500 one year ago equivalent to P600 today?
Given: F = P600 P = P500 I = 100 t = 1 year
Solution: r = 100/(500)(1)
r = 0.20 or 20% interest rate
Determine the principal that would have to be invested to provide P200 simple interest at the end of 18 months if the interest rate is 7.5%.
Given: I = P200 r = 7.5% or 0.075
t = 18 months (18/12 or 1.5)
Solution: P = 200/(0.075)(1.5)
P = P1,777.78
How long will it take for an investment of P5, 000 to grow to P7, 500 if it earns 10% simple interest per year?
Given: F = P7,500 P = P5,0000
I = P2,500 r = 10% or 0.10
Solution: t = 2,500/(5,000)(0.10)
t = 5 years
Anastasia-Grey Company deposited P100, 000 in a bank account on Oct 12 and withdraws a total of P115,000 exactly on October 12 of the next year. What is the annual interest rate at which the company was paid?
Given: P = P100,000 F = P115,000
I = P15,000 t = 1 year
Solution: r = 15,000 / (100,000) (1)
r = 0.15 or 15%
based on 360 day per calendar year
ORDINARY INTEREST
based on 365 day per calendar year
EXACT INTEREST
based on actual / exact number of days per month. (ex. January 31 days, February 28 or 29 days for leap year, March 31and so on)
ACTUAL TIME
it assumes 30 days per month
APPROXIMATE TIME
Determine the simple interest earned if P3,500 is invested at 15% interest rate in 245 days (Using exact and ordinary interest)
Given: P = P3,500 r = 15% or 0.15 t = 245
Solution:
Using exact interest
Ie = 3,500 (0.15) (245/365)
Ie = P352.40
Using ordinary interest
Io = 3,500 (0.15) (245/360)
Io = P357.29
Find the exact interest on a 120-day loan of P75,000 if the interest rate is 9 ¾%?
Given: P = P75,000 r = 9 ¾% (9.75% or 0.0975)
t = 120/365 (exact)
Solution: I = (75,000) (0.0975) (120/365)
I = P2,404.11
Determine the exact number of days from March 27, 2020 to December 20, 2021.
By listing: Count the exact number of days per month for 2010 then add 365 for 2011
March – 4 Aug – 31
April – 30 Sept – 30
May – 31 Oct – 31
June – 30 Nov – 30
July – 31 Dec – 20
plus 1 year = 365
TOTAL: 633 DAYS
Find the ordinary interest on a 120-day loan of P750,000 if the interest rate is 9 ½ %?
Given: P = P750,000 r = 9 ½% or 0.095
t = 120/360
Solution: I = (P750,000) (0.095) ( 120/360)
I = P23,750.00
Determine the exact number of days from Dec.20,2019 to Oct. 2, 2020. (Considering that 2020 is a leap year)
- To complete December 2018 = 11 days more
January 1 – September 30, 2019 = 274 days
October 2, 2019 = 2 days
TOTAL = 287 DAYS
The process of finding the present value of a given amount that is due on a future date and includes a simple interest is called discounting at simple interest, or commonly, the simple discount method. In other words, to discount an amount by the simple interest process is to find its present value.
SIMPLE DISCOUNT
➜ FORMULAS:
D =
F =
d =
t =
P =
D = represents the amount of SIMPLE DISCOUNT; Bank discount (interest taken in advance)
F = represents the MATURITY VALUE
d = represents the INTEREST DISCOUNT RATE (Interest rate for interest taken in advance)
t = represents the TERM FOR THE LOAN (in years)
P = proceeds/present value of the loan
D = Fdt
F = D / dt
d = D / Ft
t = D / Fd
P = F - D
P = F (1 – dt)
Discount P5,875 at 12% simple discount for 4 months. Find P.
Given: F = P5875 d = 12% or 0.12 T = 4/12
Solution:
D = FdT
= (5875) (.12) (4/12)
D = P235
P = 5875 - 235
P = P5,640
How much interest will be deducted from a loam worth P20,000 after 3 years with a discount rate of 6%? How much will the proceeds of the loan be?
Given: F = P20,000 d = 6% or 0.06 t = 3 years
Solution:
D = 20,000 (0.06) (3)
D = P3,600
P = 20,000 – 3,600
P = P16,400
Sam wants to borrow P12,000 payable in two years at 12% discount rate. How much will Sam receive on the origin date? How much will he pay on the maturity date?
Given: F = P12,000 d = 12% or 0.12 t = 2 years
Solution:
P = F (1-dt)
= P12,000 [ 1 – (0.12)(2) ]
P = P9,120
*Sam will receive P9120 on the origin date. However, he would pay P12,000 on the maturity date since the interest has already deducted in advance.
Compound Interest
- interest that is computed on the sum of the original principal of a deposit or loan and the interest accumulated.
-Interest earned per period is automatically reinvested to earn more interest.
-The rate of interest may be compounded once, twice, or several times in a year.
is the number of times that the interest is computed for the span of 1 year.
Frequency of conversion (m)
is the product of the frequency of conversion and the number of years. ; n = tm
Total number of conversion periods for the entire term (n)
is the rate charged which may be converted several times per year.
Nominal rate
the total interest earned for the entire term.
Compound Interest
Compound amount or accumulated value of P at the end of the term
Future Value (F)
original principal
Present value (P)
interest rate per period
Interest rate (i):
n
Number of conversion period
does not take into account the compounding period.
nominal interest rate
does take the compounding period into account and thus is a more accurate measure of interest charges.
effective interest
If Mrs. De Leon invested P12,900 for 4 years in a bank that pays 3% compounded semi-annually, how much will she receive after 4 years? How much interest will Mrs. De Leon’s investment earn?
Given: P = P12,900 t = 4 years
m = 2 j = 3% or 0.03
Solution:
i = 0.03/2 = 0.015 n = 4 (2) = 8
F = P (1 + i)n
F = P12,900 (1 + 0.015)8 = P14,531.75
I = P14,531.75 – P12,900 = P1,631.75
*De Leon will receive P 14,531.75 after 4 years. Her investment will earn total interest of P1,631.75 after 4 years.
What is the present value of P35,000 due in 7 years and 6 months if the rate is 12% compounded quarterly?
Given: F = P35,000 t = 7.5 years
m = 4 j = 12% or 0.12
Solution:
i = 0.12 / 4 = 0.03
n = (7.5) (4) = 30
P = F ( 1 + i )-n
P = P35,000 ( 1 + 0.03 )-30
P = P14,419.54
*The present value of P35,000 that is due at the end of 7.5 years is P14,419.54
How much do you need to invest now, to get P10,000 in 10 years at 8% interest rate?
Solution:
P = P10,000(1+0.08)-10 = 10,000 (2.1589)
P = P4,631.93
So, P4,631.93 invested at 8% for 10 Years grows to $10,000
You take out a P1,000 loan for 12 months and it says 1% per month, how much do you pay back?
Just use the Future Value formula with “n” being the number of months:
Solution: F = P (1+r)n
= P1,000 × (1.01)12
= P1,000 × 1.12683
F = P1,126.83 to pay back
At 6% interest with monthly compounding does not mean 6% per month, it means 0.5% per month (6% divided by 12 months), and is worked out like this:
Solution: F = P (1+r/n)n
= P1,000 (1 + 0.06/12)12
= P1,000 (1 + 0.005)12
= P1,000 (1.005)12
= P1,000 × 1.06168…
F = P1,061.68 to pay back
*This is equal to a 6.168% (P1,000 grew to P1,061.68) for the whole year.
Example: you have $1,000, and want it to grow to $2,000 in 5 Years, what interest rate do you need?
The formula is: r = ( F / P )1/n - 1
Note: the little “1/n” is a Fractional Exponent (radicals or rational exponent). first calculate 1/n, then use that as the exponent on your calculator.
For example 20.2 is entered as 2, “x^y”, 0, ., 2, =
Now we can “plug in” the values to get the result:
Solution: r = (P2,000 / P1,000)1/5 – 1
= (2)0.2 – 1
= 1.1487 − 1
r = 0.1487 and 0.1487 or 14.87%
*So you need 14.87% interest rate to turn $1,000 into $2,000 in 5 years.
What interest rate do you need to turn P1,000 into P5,000 in 20 Years?
Solution: r = (P5,000 / P1,000)1/20 – 1
= (5)0.05 – 1
= 1.0838 – 1
r = 0.0838 and 0.0838 or 8.38%.
*So 8.38% will turn $1,000 into $5,000 in 20 Years.
You want to know how many periods it will take to turn P1,000 into P2,000 at 10% interest.
This is the formula (note: it uses the natural logarithm function ln):
Solution: n = ln(F / P) / ln(1 + r)
The “ln” function should be on a good calculator.
You could also use log, just don’t mix the two.
Anyway, let’s “plug in” the values:
n = ln( P2,000/P1,000 ) / ln( 1 + 0.10 )
= ln(2)/ln(1.10)
= 0.69315/0.09531
n = 7.27
*It will need 7.27 years to turn P1,000 into P2,000 at 10% interest.
How many years to turn P1,000 into P10,000 at 5% interest?
Solution: n = ln( P10,000/P1,000 ) / ln( 1 + 0.05 )
= ln(10)/ln(1.05)
= 2.3026/0.04879
n = 47.19
*47 Years. But we are talking about a 10-fold increase, at only 5% interest.
Designed, produced, and marketed by a vendor and sold by many retailers.
National (Manufacturer) Brands
Developed by a retailer and only sold in the retailer’s outlets.
Private-Label (Store) Brands
comparable to, even superior to, manufacturer’s brand quality, with modest price savings Ex. Walmart, Tesco
What type of category of private brands is this?
PREMIUM
target a price sensitive segment by offering a no-frills product discount.
What type of category of private brands is this?
GENERIC
imitate the manufacturer’s brand in appearance and packaging, perceived as lower quality, offered at lower price.
What type of category of private brands is this?
COPYCAT
eveloped by a national brand vendor and sold exclusively by the retailer. Difficult for consumers to compare prices for virtually the same product.
What type of category of private brands is this?
EXCLUSIVE CO BRANDS
Relative Advantages of Manufacturer vs. Private brands
National Brands (NB); Private Label Brands (PLB)
Impact on a store:
Store Loyalty: (NB = ?) ; (PLB= +)
Store Image: (NB= +); (PLB= +)
Traffic Flow: (NB= +); (PLB= +)
Selling and Promotional Expenses: (NB= +); (PLB= -)
Restrictions: (NB= -); (PLB= +)
Differential Advantages: (NB= -); (PLB= +)
Margins: (NB= ?); (PLB= ?)
National (Manufacturer) Labels
(Advantages and Disadvantages)
ADVANTAGES
- Help retailers build their image and traffic flow
- Reduces selling/promotional expenses
- More desired by customers
- Customers patronize retailers selling the branded merchandise
- Large retailers can push some of the financial risk of buying merchandise back onto the vendor
DISADVANTAGES
-Lower margins
-Vulnerable to competitive pressures
-Limit retailer’s flexibility
Private Labels
(Advantages and Disadvantages)
Advantages
-Unique merchandise not available at competitive outlets
-Exclusivity boosts store loyalty
-Difficult for customers to compare price with competitors
-Higher margins
Disadvantages
-Require significant investments in design, global manufacturing sourcing
-Need to develop expertise in developing and promoting brand
-Unable to sell excess merchandise
-Typically less desirable for customers
Buying decision for fashion apparel/accessories:
- 5-6 times a year
- Many months before delivery
- Withhold open-to-buy (OTB) for new items with fashion change
Buying decision for staple merchandise:
- Less frequent
- Continuous replenishment
Wholesale Market Centers
National Markets (New York), Regional Markets (Dallas, Atlanta, Miami), London, Milan, Paris, Tokyo
National Markets (New York), Regional Markets (Dallas, Atlanta, Miami), London, Milan, Paris, Tokyo
Trade Shows
Frankfurt Book Fair, Las Vegas Consumer
Electronics Show, Atlanta Super Show for Sporting Goods, Internet Exchanges
Worldwide Retail Exchange
Meeting Vendors at Your Company
National Brand Buying Process
-Meet with vendors
-Discuss performance of vendor’s merchandise during the previous season
-Review the vendor’s offering for the coming season
-May place orders for the coming season
-Sometimes they do not buy at market, but review merchandise, return to their offices to discuss with the buying team before negotiating with vendors
In-House
Large retailers (e.g., JCPenney, Macy’s, The Gap, American Eagle Outfitters) have divisions specialized in
- identifying trends, designing, specifying products
- Selecting manufacturers
- Monitoring and managing manufacturing conditions and product quality
Limited Brands acquired MAST Industries
Acquisition
- one of the world’s biggest contract manufacturers, importers, distributors of apparel
- Have manufacturing operations and join ventures in 12 countries
- Also provides private label merchandise for Abercrombie & Fitch, Lane Bryant, New York & Company, Chico’s
MAST
ex. Li & Fung – partnered with many specialty retailers
Outsource
After decisions are made on what and how much private-label merchandise will be acquired,
Designers develop specifications
Sourcing departments find a manufacturer, negotiate a contract, and monitor the production process, or
Use Reverse Auctions to get quality private-label merchandise at low prices
Resident Buying Services – include
Reports on market and fashion trends
Assistance with merchandise budget and assortment plans
Assistance in order placement, adjustments with vendors
Introduction to new resources
Import purchases
Exclusivity of merchandise (private-label and special purchases)
Arrangement of vendor appointments
Example: The Doneger Group
Retail Exchange
Internet-based solutions and services for retailers
Example: Agentrics, WorldWide Retail Exchange (WWRE), GlobalNetXchange (GNX)
The Robinson-Patman Act (Anti-Chain-Store Act)
What type of legal and ethical issues for buying merchandise is this?
Purchase Terms and Conditions
The Robinson-Patman Act (Anti-Chain-Store Act)
-Restricts the prices and terms that vendors can offer to retailers
-Forbid vendors from offering different terms and conditions to different retailers for the same merchandise and quantity
Different prices can be offered if:
The cost of manufacturing, selling, and delivery are different
The retailers are providing different functions (distribution, store service, etc.)
A requirement imposed by a vendor that a retailer cannot sell an item for less than a specific price- the manufacturer’s suggested retail price(MSRP)
Resales Price Maintenance (RPM)
For ensuring adequate margin for retailers, but some retailers do not appreciate RPM to have the flexibility on pricing
Reduces free riding of discount stores
Is legal (was illegal in the past for obstructing competition) as long as it promotes Interbrand competition and restricts intrabrand competition
Commercial Bribery
A vendor or its agent offers to give or pay a retail buyer “something of value” to influence purchasing decisions.
A fine line between social courtesy of a free lunch and an elaborate free vacation
Some retailers with a zero tolerance policy
Some retailers accept only limited entertainment or token gifts
Chargebacks
A practice used by retailers in which they deduct money from the amount they owe a vendor without getting vendor approval
Two reasons:
- merchandise isn’t selling
- vendor mistakes
Difficult for vendors – Disrupt relationships
Buybacks
Used to get products into retail stores
Two scenarios:
Retailer allows a vendor to create space for its goods by “buying back a competitor’s inventory and removing it from retailer’s system
Retailer forces a vendor to buyback slow-moving merchandise
- Goods made and sold without the permission of the owner of a trademark, a copyright, or a patented invention that is legally protected in the country where it is marketed
- Major problem is counterfeiting intellectual property
Counterfeit Merchandise
-possess a valid U.S. registered trademark and is made by a foreign manufacturer but is imported into the United States without permission of the U.S trademark owner.
-Not counterfeited
-is legal
Gray Market Merchandise (parallel imports) -
similar to gray-market merchandise except there need not be distribution across boundaries.
Diverted Merchandise
Occur when a manufacturer or wholesaler restricts a retailer into carrying only its products and nothing from competing vendors
Ex. Safeway – Coca cola
Illegal when they restrict competition
An agreement that requires the retailer to take a product it doesn’t necessarily desire (the tied product)to ensure that it can buy a product it does desire(the tying product)
Illegal when they lessen competition
Ok to protect goodwill and quality reputation of vendor- legal for a vendor to require a buyer to buy all items in its product line
Tying Contract
