BMAT 230
Business Mathematics
Case Study
Case Study 9 B
1
BMAT 230 Business Mathematics
Adapted from L. Daisley, T. Kugathasan and D. Huysmans
Mathematics of Business and Finance, 4th Edition,
Vretta, 2020
Borrowing to Start a Business
Enea, a promising entrepreneur, was excited for being recognized as having the best business
plan at her college's annual entrepreneurial competition. An angel investor was so impressed
with her plan that he offered her a loan at 6% compounded semi-annually to start her designer
clothing store. After two years, her business had savings of $80,654 and she used the entire
amount to completely pay off her outstanding debt with the investor.
a)
What was the loan amount provided to her by the investor and what was the accumulated
interest over the two- year period?
b)
What is the Nominal Rate, compounded monthly, (to four decimal places) would have
resulted in the same accumulated debt?
c)
If Enea did not pay any amount throughout the term and the interest rate had remained at
6% compounded semi-annually, how long (in years and days) will it take for the debt to
reach $100,000?
d)
If she had obtained the same loan amount from a local bank, it would have accumulated
to $80,654 in 18 months instead of two years. What is the interest rate compounded semi-
annually charged by the local bank?
e)
Calculate the loan amount provided to her by the investor if the loan had been issued to
her at an annually compounding frequency instead of a semi-annually compounding
frequency. Compare your answer to (a) and determine what her savings would be.
f)
If her contract with the investor required that she settle all dues in two years, how much
could she have borrowed initially if she was sure that she could repay $25,000 in one
year and $40,000 at the end of two years?
g)
What was the size of the loan provided by the investor if she was charged 6%
compounded semi-annually for the first year and 8% compounded quarterly for the
second year, and it accumulated to $80,654 in two years?
