Thalia, Georgia, and Fariyal started a cupcake business in their final year in college, registering the company as 'Sugary

Bites'. They needed measuring cups, mixers, a food processor, and other baking equipment to prepare for production.

This equipment cost a total of $$1500,$ which the entrepreneurs financed through a loan from a bank at $12\mathrm{.}5\%$ compounded

monthly, amortized over two years. Within a week, they started making cupcakes and delivering them to their college

cafeteria.

Within two months, Sugary Bites was the talk of the college campus and the bakery business was making modest profits.

After graduating, the three budding entrepreneurs decided to expand their operation. They rented a retail store in the city

and added ten new cupcake flavours to their product line. They also hired an assistant to run the store and a delivery person

to handle personal orders.

After two years of successfully managing Sugary Bites, they saved enough money to use as a down payment to purchase a small

shop where they could make their cupcakes, and a delivery truck to deliver them. They identified a $$108,000$ commercial property

and secured a mortgage for $80\%$ of its value to purchase it$.$ The fixed interest rate on the mortgage was $3\mathrm{.}4\%$ compounded semi$-$

annually for an amortization period of five years. They also purchased a delivery truck for the business at a cost of $$18,500$ and

financed $80\%$ of it at $7\%$ compounded monthly. They made monthly payments of $$300$ towards this loan.

Answer the following questions related to each of their debts:

Startup Loan

a$.$ What were their monthly payments to settle this loan?

b$.$ What was the principal balance on the loan after one year?

c$.$ Construct an amortization schedule for this loan.

Mortgage

d$.$ Calculate the size of their monthly payments rounded to the next $$10.$

e$.$ By how much would their amortization period shorten if they paid the rounded payment from $($d$),$ then also made

a lump sum payment of $$10,000$ at the end of the third year of the mortgage, and finally increased their periodic

payment by $30\%$ after the ${40}^{th}$ payment?

Delivery Truck Loan

f$.$ How long would it take to settle this loan with regular monthly payments of $$300?$

g$.$ On their ${20}^{th}$ payment, what will be the interest portion and what will be the principal portion?

h$.$ Construct a partial amortization schedule showing details of the first two payments, last two payments, total payment

made, and the total interest paid towards this loan.