Business Mathematics: Analyzing Loans, Investments, and Returns

This assignment analyzes a business case involving two classmates, Shing and Benjamin, who start a video game company and secure a loan. The assignment delves into calculating the total amount paid to settle the initial bank loan, determining the amounts invested by Shing in a T-bill and an interest-bearing promissory note, and calculating Benjamin's investments in a non-interest-bearing promissory note and a loan to a friend. Further calculations include the proceeds from Shing's investments after discounting his promissory note, determining the interest rate Benjamin should charge his friend to match Shing's earnings, and calculating the time it takes for Benjamin's investment to double at that interest rate. The solution provides detailed calculations and explanations using simple interest formulas, covering various investment scenarios and financial decisions.

Running head: BUSINESS MATHEMATICS 1
CASE 8a: Borrowing and Investing Using Simple Interest
By (Name of Student)
(Institutional Affiliation)
(Date of Submission)

BUSINESS MATHEMATICS 2
Shing and Benjamin, two classmates at a college, decided to use their free time after
classes to create video games. On October 07, 2016, they received a loan of $3000 from a
bank at 8.5% p.a. to start their small business. Two months later, they launched their first game
in the community and it was highly successful. On March 02, 2017, a larger gaming company
paid them $50,000 to purchase copyrights to their game. Shing and Benjamin used $5000 from
this amount to settle the bank loan and to cover other miscellaneous expenses.
They then shared the balance of $45,000 equally between themselves.
Shing invested a portion of it in a 182-day T-bill that had an interest rate of 4% p.a. and a face
value of $7500 and used the balance in a 270-day interest-bearing promissory note at 6% p.a.
Benjamin, on the other hand, invested a portion of it in a 270-day non-interest-bearing
promissory note that had an interest rate of 5% p.a. and a face value of $9000, and loaned the
balance to his friend, who was running a successful website-design business, for 182 days.
a. Calculate the total amount they paid to settle the bank loan.
Total amount used in settling bank loan is given by the formula;
A = P (1 + rt) where t= time which is 1 year in this case
Total amount paid = 3000 × 108.5/100
= $ 3255
b. i) Calculate the amounts that Shing invested in the T-bill and in the interest-bearing
promissory note.
By letting the amount that Shing invested in the T-bill and the interest-bearing to be Y,
22,500 = (182/365 × 0.04) Y + $ 7500 + (270/365 × 0.06) Y
Y = $ 12,500
Thus the amount invested by Shing in the T-bill and the interest-bearing promissory note
is $ 12,500
ii) Calculate the amount that Benjamin invested in the non-interest-bearing promissory
mount that he loaned to his friend.
Portion of $ 22,500 to 27 day non-interest bearing promissory note3.
$22,500 × 270/365 × 0.85= $ 14147.30
Thus the amount = $ 14147.30
c. Shing decided to discount his interest-bearing promissory note at the time of
maturity of his T-bill (182 days) and used the money to purchase a car for himself.
Calculate the total proceeds from his investments if he discounted his interest-bearing
promissory note at 6.50% p.a.
Shing’s interest bearing promissory note at the time of maturity of his T-bill of 182 days
is given by;
$ (22,500) ×182/365 × 0.065 = $ 729.20
The total proceed from his investments if he discounted at the rate of 6.50% is thus
=$(729.20 + 7500 +12,500)
= $ 20,729.20
d. Benjamin wants to have the same amount as Shing in 182 days. If he discounts his non-
interest-bearing promissory note at 7% p.a., what interest rate should he charge his friend
for the loan?

BUSINESS MATHEMATICS 3
Total amount needed by Benjamin is equal to Shing’s amount = $ 20,729.20 and in 182 days.
By letting the interest rate to be R, we have;
$20, 729.20 = R × 182/365 + 7/100 × 14147.30
R = 9% per annum.
e. If Benjamin invested his initial share at the interest rate that he loaned to his friend
(determined from (d)), how long would it take for his investment to double?
Given that the initial share was $22,500, and by using the interest rate of 9% obtained in part
d above, we determine the time given also that the investment should double.
The amount of investment when doubled should be 2 × 14147.30 = $28294.60
Thus $28294.60 = $ 22,500 × t ×1.09
Time = 1.153 years which when converted to days approximately becomes 421 days
References
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Mild, A., Waitz, M., & Wöckl, J. (2015). How low can you go?—Overcoming the inability
of lenders to set proper interest rates on unsecured peer-to-peer lending
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