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Requirement
1. A retailer paid $53.69 for a set of utensils. Overhead is 13.5% of the regular selling price and profit is 151 2 % of the regular selling price. During a clearance sale, the set was sold at a markdown of 18%. What was the operating profit or loss on the sale?
2. A merchant receives an invoice for $7600 with terms 4/10, n/90. (a) What is the highest simple interest rate at which he can afford to borrow money in order to take advantage of the discount? (b) If he can borrow money at 9.5%, how much can he save?
3. A 6-month note dated March 31, 2008, promises to pay Mr. Smith $8700 plus simple interest at 11%. On May 12, 2008, it is sold to a bank that discounts notes at a 8.5% simple interest rate. (a) Find the maturity date and maturity value of the note. (b) What is the purchasing price of the bank? (c) What rate of interest does Mr Smith realize?
4. On July 1, $50,000.00 364-day treasury bills were auctioned off to yield 3.97%.
a)What is the price of each $ 50,000.00 T-bill on July 1?
(b)What is the yield rate on Sept 30 if the market price is $49,307.97?
(c)Calculate the market value of each $ 50,000.00 T-bill on November 19 if the rate of return on that date is 2.34%.
(d)What is the rate of return realized if a $50,000.00 T-bill purchased on July 1 is sold on January 23 at a market rate of 3.41%?
5. Mr. Story opened an RRSP deposit account on Oct 1, 2010, with a deposit of $2400. He added $3100 on Sept 1, 2012, and another $4000 on July 1, 2014. How much will be in his account on Dec 1, 2018, if the deposit earns 5.3% p.a. compounded monthly?
6. $14 000 was deposited into an investment account for eight years earning interest at a nominal rate of 8% p.a. compounded monthly. How much interest was earned in the third year?
7. A seven-year note for $4 378.67 issued on Aug 1, 2004, with interest at 6% compounded quarterly is discounted on May 1, 2010, at 2.9% compounded semi-annually. What are the proceeds of the note?
8. JK Books owes $8000 due in two years with interest at 11% compounded semi-annually and $6 500 due with interest in fifteen months at 9% compounded quarterly. If the company wants to discharge these debts by making two equal payments, the first now and the second eighteen months from now, what is the size of the two equal payments if money is now worth 8.4% compounded monthly?
Solutions
Solution to Question 1
As the question is not aligned correctly, the following assumption is made
Profit is 2% of the regular selling price
Also given, Overhead is 13.5% of the regular selling price
Therefore, selling price of the utensil is $53.69 + 13.5% of Selling Price (Overhead Cost) + 2% of Selling Price (Profit)
SP = $53.69 + 13.5%(SP) + 2%(SP)
On solving, SP = $63.54
Operating Profit or Loss on Sale:
Product sold at markdown of 18% of SP, which is $63.54 – 18% (63.54) = $52.10
Therefore, Operating Profit/Loss on sale = $52.10 - $53.69 – 13.5%(63.54) = $10.17 (Loss)
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Solution to Question 2
4/10, n/90, This means that the credit period is 90 days and if the Invoice is paid within 10 days, discount received shall be 4% of the Invoice value.
Highest simple interest rate shall be the rate at which the discount received shall be equal to the simple interest on the borrowing amount which is computed as follows:
Discount = $7600 *4% = $304, which shall be the simple interest for the bill period of
90 days on $7,600. No of days in a year is taken at 360 days.
Therefore, the simple interest rate shall be:
$304 = $7,600 * x% * (90/360)
On solving, Simple interest rate shall be 16%.
If borrowed at 9.5%, savings shall be the excess of Discount over Interest paid which is computed as follows:
Interest = $7,600*9.5%*(90/360) = $180.5
Therefore, Savings = $304 - $180.5 = $123.5
Solution to Question 3
Maturity date of the note = 6 months from 31 March, 2008 which is 30 September, 2008.
Maturity Value of the note is computed as follows:
Maturity Value = Principal + (Principal * Rate of Interest * Time Period)
= $8,700 + $8,700*11%*6/12
= $9,178.5
Purchasing Price of the Bank shall be computed as follows:
Time period left for maturity of the note = 12 May 2008 to 30 September 2008 = 142 days.
Maturity Value = Principal + (Principal * Rate of Interest * Time Period)
$9,178.5 = P + P *8.5% * (142/360)
$9,178.5 = P * (1 + 0.0335)
Therefore, Purchasing Price of the Bank = $8,881
Rate of Interest realised by Mr Smith shall be calculate as follows:
Interest Amount received = $8,881 - $8,700 = $181 for the period of 41 days.
Maturity Value = Principal + (Principal * Rate of Interest * Time Period)
$8,881 = $8,700 + ($8,700 * Rate of Interest * 41/360)
$181 = $990.83 * Rate of Interest
Rate of Interest = 18.26%
Solution to Question 4
Computation of each sub question is made in terms of the question solved under sub-section (a)
Price of each T-Bill on July 1,
We know that Discount Yield = [ (Face Value – Purchase Price) / Face Value ] * [364/Maturity of the Bill]
3.97% = [ ($50,000 – Purchase Price] / $50,000] * [364/364]
3.97% * $50,000 = $50,000 – Purchase Price
Therefore, Purchase Price = $50,000 – (3.97%*$50,000) = $48,015
Yield rate on 30 September if Market Price is $49,307.97,
We know that Discount Yield = [ (Face Value – Purchase Price) / Face Value ] * [364/Maturity of the Bill]
= ($50,000 - $49,307.97) / $50,000 * (364/273)
= 1.84%
Market Value of each T-Bill on November 19 if rate of return is 2.34%
We know that Discount Yield = [ (Face Value – Purchase Price) / Face Value ] * [364/Maturity of the Bill]
2.34% = [ ($50,000 – Purchase Price) / $50,000 ] * (364/223)
$716.79 = $50,000 – Purchase Price
Therefore, Market Value = $49,283.21
Rate of return realised on January 23,
3.41% = [ ($50,000 – Purchase Price) / $50,000 ] * (364/158)
$740.08 = $50,000 – Purchase Price
Therefore, Market Value = $49,259.92
Realised Amount = $49,259.92 (Purchase Price) - $48,015 (Sold Price)
Realised Amount = $1,244.92
Realised Rate computed as follows:
$49,259.92 = $48,015 + ($48,015 * Rate of Interest * 207/360)
Rate of Interest = 4.51%
Solution to Question 5
Under Compound Interest, computation of interest is made on Interest as well. Formula for the same is
Future Value = Principal * (1 + (annual interest rate/number of times compounded in a year)) ^ (number of times compounded in a year*time period)
October 1, 2010 to September 1,2012 = 23 months = 1.92 years
Future Value of $2,400 compounded at 5.3% p.a compounded monthly,
$2,400 * (1+ (5.3%/12)) ^ (12*1.92)
Value of $2,400 on October 1, 2010 including interest component compounded = $2,656.50
September 1,2012 to July, 1 2014 = 22 months = 1.83 years
Future Value of $2,656.5 + $3,100 = $5,756.5 compounded at 5.3% p.a compounded monthly,
$5,756.5 * (1+ (5.3%/12)) ^ (12*1.83)
Value of $5,756.5 on July 1,2014 including interest component compounded = $6,341.44
July 1,2014 to December, 1 2018 = 53 months = 4.42 years
Future Value of $6,341.44 + $4,000 = $10,341.44 compounded at 5.3% p.a compounded monthly,
$10,341.44 * (1+ (5.3%/12)) ^ (12*4.42)
Value of $10,341.44 on December 1, 2018 including interest component compounded = $13,064.60
Solution to Question 6
Under Compound Interest, computation of interest is made on Interest as well. Formula for the same is
Future Value = Principal * (1 + (annual interest rate/number of times compounded in a year)) ^ (number of times compounded in a year*time period)
Value of Investment at the end of 2nd year =
$14,000 * (1+(8%/12))^(12*2) = $16,420.4
Value of Investment at the end of 3rd year =
$14,000 * (1+(8%/12))^(12*3) = $17,783.3
Therefore Interest earned in the third year = $17,783.3 - $16,420.4 = $1,362.9
Solution to Question 7
Under Compound Interest, computation of interest is made on Interest as well. Formula for the same is
Computation of Value of Note as on 1 May, 2010:
Future Value = Principal * (1 + (annual interest rate/number of times compounded in a year)) ^ (number of times compounded in a year*time period)
From August 1,2004 to May 1, 2010 , no of quarters = 69 months / 4 = 17.25 quarters
Value of Seven year note as at May 1,2010 =
$4,378.67 * (1+(6%/4))^(4*17.25) = $12,232
Computation of Proceeds of Note as on 1 May, 2010:
Maturity date of the note = 7 years from 1 August, 2004 which is 1 August, 2011.
Time left for maturity = May 1, 2010 to August 1, 2011 = 15 months for maturity
Proceeds of the note on May 1, 2010 =
Face Value of the Note = $4,378.67 * (1+(6%/4))^(4*21) = $15,292.9
$15,292.9 = Note Proceeds * (1+(2.9%/2))^(2*2.5)
Note Proceeds = $14,230.81
Solution to Question 8
Under Compound Interest, computation of interest is made on Interest as well. Formula for the same is
Computation of Present Value of Debt of $8,000 with 11% interest compounded semi-annually:
Future Value = Principal * (1 + (annual interest rate/number of times compounded in a year)) ^ (number of times compounded in a year*time period)
= $8,000 * (1+((11/100)/2))^(2*2)
= $9,910.59
Computation of Present Value of Debt of $6,500 with 9% interest compounded quarterly:
Future Value = Principal * (1 + (annual interest rate/number of times compounded in a year)) ^ (number of times compounded in a year*time period)
= $6,500 * (1+((9/100)/4))^(4*3.75)
= $9,075.34
Total Due along with Interest = $9,910.59 + $9,075.34 = $18,985.93
Computation of 2 Equal Instalments =
Let X be the Instalment Amount
$18,985.93 = X + X * ((1+(8.4%/12))^ (12*1.5)
2.13378X = $18,985.93
Therefore, Instalment Amount = $8897.77
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Compound Interest Formula - Explained. (2016). Thecalculatorsite.com. Retrieved 11 October 2016, from http://www.thecalculatorsite.com/articles/finance/compound-interest-formula.php
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Estimating Yields on Treasury Securities. (2016). Newyorkfed.org. Retrieved 11 October 2016, from https://www.newyorkfed.org/aboutthefed/fedpoint/fed28.html
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Simple Interest Important Formulas - Aptitude Questions and Answers. (2016). Indiabix.com. Retrieved 11 October 2016, from http://www.indiabix.com/aptitude/simple-interest/formulas
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SOLUTION: An invoice of $2,000 is dated November 10, and terms of 4/10. n/30 are being offered. Find the cash discount and the amount due if the invoice is paid within 10 days.. (2016).Algebra.com. Retrieved 11 October 2016, from https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.168918.html
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