Question $2-(25$ points$)$

Consider a loan of $100,000$ with a repayment period of $15$ years and a fixed annual interest rate of $5\%.$ The loan installments are to be paid quarterly.

What is the quarterly installment amount?

How much interest will be paid over the entire $15-$year loan term?

What is the flat rate for the loan?

After $3$ years, a new repayment plan is implemented due to an increased interest rate. The new effective interest rate is set at $6\mathrm{.}5\%.$

Using the perspective approach, what is the residual debt at the end of the $6$ th year, according to the new repayment plan?

A real estate firm is evaluating the feasibility of investing in a new property development project. The company has the opportunity to purchase the land for $1,000,000$ on January $1,2025.$ The Overall construction and development expenses are projected to be $64,000,000,$ which will be paid in eight equal monthly installments in advance, starting on June $1,2025.$

The construction phase will end on September $1,2026,$ and rental income is expected to begin flowing in from December $1,2026,$ with revenue being recelved every quarter in advance. The projected remal earnings amount to $C200,000$ per quarter. Meanwhile, operational costs, including property management and upkeep, are anticipated to be $620\mathrm{.}000$ per quarter, payable In adrance starting from December $1,2026.$

It is assumed that all costs and revenues will come to an end by September $2036.$

Calculate the net present valye and accumblated value of the project, assuming a discount rate of $4\%.$

Using Excel or $R,$ simulate $1,000$ scenarios of interest rates uniformly distributed between $1\%$ and $7\%,$ and calculate the expected net presens value and accumulated value of the project. Additionally, determine the probability that the net present watue exiceeds the expected values computed in $1.$