Consider that $2,500$ dollars today are worth more than $2,500$ dollars in four years. This is because you can take $2,500$ dollars today and invest it at a rate of $5\%$ each year. Calculate Net Present Value $($NPV$).$

Consider that $12,600$ dollars today are worth more than $12,600$ dollars in five years. This is because you can take $12,600$ dollars today and invest it at a rate of $7\%$ each year. Determine Net Present Value $($NPV$).$

One student needs $1,000$ dollars now and promised to pay you back $1,000$ dollars in a year. Is that a fruitful investment when you can invest at $9\%$ elsewhere?

Suppose a project requires an initial investment of $10,200$ dollars and is expected to generate a cash flow of $100$ dollars for five years plus $15,000$ dollars in the third year. The target rate of return of the project is $9\%$ per year. Calculate the net present value of the project.

Louis Palmieri invested $27,500$ dollars in a high$-$yield account. At the end of $30$ years, he closed the account and received $525,350.$ Compute the internal rate of interest $($IRR$).$