# All work must be shown on every facet of the solution. This includes a timeline with cashflows,

## Question:

**All work must be shown on every facet of the solution. This includes a timeline with cashflows, timing and rates clearly laid out and formulas (in pure form, not in the calculator or excel form). A detailed timeline and formulas are both required. Please do not attempt to show work by providing calculator steps. The actual equations are required to receive credit for answers, even if correct. Correct answers without proper work shown in enough detail will be marked wrong. Incorrect answers with proper work and methods outlined correctly will be graded positively with partial credit.**

1. Please use the lump sum approach to calculate the present value of an ordinary three-year annuity, where payments are seventy dollars each. Map out each step very clearly. Use r=0.06 (quarterly compounded).

What would happen if these payments were "due"? Explain in equation format as well as in words. Makes sure to explain the reasoning behind this as well.

2. The design studio you rented requires you to sign a lease for 60 months, at seven thousand dollars monthly, with the first payment due today. At an APR of .0524 (monthly compounding), what is the present value of the entire stream of payments you will have to make?

3. Nine years ago, Beatrice invested a sum of $6,000. The interest rate she earned changed over time: During the first three years, she earned 5 percent annually compounded, during the following two years she earned 8 percent compounded semiannually, and during the final three years, she earned 10 percent continuously compounded. Find the value of this investment at the end of the 8^{th} Show all work.

4. What will you pay today for an infinite annuity that will pay $3,000 each year, if the first payment occurs in precisely seven years? Assume an interest rate of 9 percent?

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