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 off her outstang

debt with the investor.

a$.$ What was the loan amount provided to her by the angel investor and what was the accumulated interest over the two$-$

year period?

b$.$ What rate, compounded monthly, 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 angel 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?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 off her outstang

debt with the investor.

a$.$ What was the loan amount provided to her by the angel investor and what was the accumulated interest over the two$-$

year period?

b$.$ What rate, compounded monthly, 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 angel 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?