Borrowing to Start a Business

Stephanie, 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 business by offering her a loan at $2\mathrm{.}00\%$ compounded quarterly.

After $3$ years, her business had savings of $$117,632\mathrm{.}00$ 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 angel investor and what was the accumulated interest over the three$-$year period?

PV $=$

I $=$

Round to the nearest cent.

b$.$ What rate, compounded monthly, would have resulted in the same accumulated debt?

j $=$

$\%$

Round to two decimal places.

c$.$ How long $($rounded up to the next month$)$ would it take for her debt to reach $$138,000\mathrm{.}00$ if she does not repay any amount throughout the term? Assume the same interest rate of $2\mathrm{.}00\%$ compounded quarterly throughout this extended period.

years and

months

Round up to the next month.

d$.$ If she had obtained the same loan amount from a local bank, it would have accumulated to $$117,632\mathrm{.}00$ in $32$ months instead of three years. What is the interest rate compounded quarterly charged by the local bank?

j $=$

$\%$

Round to two decimal places.

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 quarterly compounding frequency. Compare your answer to $($a$)$ and determine what her savings would be$.$

Savings $=$

Round to the nearest cent.

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 $$26,000\mathrm{.}00$ in one year and $$46,000\mathrm{.}00$ at the end of two years?

Round to the nearest cent.

g$.$ What was the size of the loan provided by the investor if she was charged $2\mathrm{.}00\%$ compounded quarterly for the first year and $4\mathrm{.}00\%$ compounded semi$-$annually for the following year$($s$)$ and it accumulated to $$117,632\mathrm{.}00$ in three years?

Round to the nearest cent.