CASE B BORROWING TO START A BUSINESS

Caileigh, a budding entrepreneur, was excited that her presentation at her college annual entrepreneurial competition was voted the best by every judge. An angel investor in the audience was very impressed by her business plan and offered to help her start her designer clothing store by offering her a loan at 5.312% compounded semi-annually. After two years, her business had savings of $84, 970 and she used the entire amount to completely pay off her outstanding debt with the investor.

1. What was the loan amount given to her by the angel investor and what was the accumulated interest over the two-year period? What rate, compounded monthly, would have resulted in the same accumulated debt?
2. What is the effective rate of the monthly compounded rate calculated in part (2)?
3. How long (in years and months, rounded up to the next month) would it take for her debt to reach$100, 000 if she does not repay any amount throughout the term? Assume the same interest rate of 5.312% compounded semi-annually throughout this extended period.
4. If she had taken the same loan amount from a local bank, it would have accumulated to $84, 970 in 18 months instead of two years. What is the interest rate compounded semi-annually charged by the local bank? If her contract with the investor required that she settles all dues in two years, how much could she have borrowed initially if she was sure that she could repay $27, 500 in one year and $43, 000 at the end of two years?