please reply if you can answer all the questions. 1. What is the present value o

Question

please reply if you can answer all the questions.

1. What is the present value of a 15-year annuity that pays $50 per year, assuming 12% annual interest rate ? _________

2. Assume you currently have $4,000. If you deposit this money in a bank account at an annual interest rate of 2.5%, and in addition deposit $500 at the end of each year for the next 7 years, how much will you have in the account after 7 years? ___________________________

3. What is the present value of receiving $500 per year forever, assuming 6% interest rate? ____________________

4. Assume you deposit $600 in an account, and that in 6 years you have $900. Assuming daily compounding frequency what is the quoted annual interest rate associated with the account? Avoid rounding until the final answer! ______________________________________

5. How many years would it take for a $100 deposit to grow to $200 at a 5% quoted annual interest rate, under monthly compounding? _____________________________________

6. Assume the annual periodic rate is equal to 14.00%, and that the compounding frequency is daily. What is the corresponding effective annual rate equal to?___________________________

please reply if you can answer all the questions.

Explanation / Answer

1. Present Value = A x (1+r)n- 1/r (1+r)n where A = Annuity ($50); r = rate of interest (12%);n = period of payments (15)

    Present value = 50 x (1+0.12)15- 1/0.12(1+0.12)15= 50 x 4.4736/0.6568 = $340.56

2. $4,000 will become = $4000 x (1+0.025)7 = 4,000 x 1.18869 = $4,754.74

      Futurre value of $500 annuity = 500 x (1+0.025)7-1/0.025 = 500 x 0.18869/0.025 = @3,773.72

     Total future vlaue = $ 4,754.74 + 3,773.72 = $8,528.46

3. Present value of constant perpetuity = C/r where C= cash flow ie. 500; r = rate of interest i.e 6%

                                                               = $500/0.06 = 8,333.33

4. 600(1+r)2,190= 900

   = (1+r)2,190 = 900 - 600 = 300

    = (1+r) = (300)1/2,190 = 1.36986301 =

  r = 0.36986301 or 36.99%; Hence, rate of interest is 36.99%

5. 100(1+0.004)n = 200 = (1.004)n = 200 -100 =100; Solve for n

6. 100(1+0.0003835)365 = this answer is the effective rate; pl.do in scientific calculator

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