Compute the unknown values for the four cash - flow diagrams shown. Your real es

Question

Compute the unknown values for the four cash - flow diagrams shown. Your real estate taxes are $3, 600 per year with one-half due April 1 and the remainder due October 1 each year. What single sum of money must you place in an account earning 5.25% interest 15 months before the first payment is due in order to accumulate enough money to pay each tax bill? Assume monthly compounding. You have just made an investment that will repay S976.12 at the end of each month; the first payment is one month from today and the last one is six years from today (thereby depleting the account), (a) If the interest rate is 6.5% per year compounded monthly, what amount did you invest? (b) If you can refuse all the payments and allow the money to earn at the same rate as stated, how much will you have at the end of six years?

Explanation / Answer

3.

So

976.12 =(P x 0.065/12 x (1+0.065/12)^(12*6) )/((1+0.065/12)^(12*6) - 1)

=> 976.12*0.4754 = P x 0.007992

=> P = $58068

a. Amount invested =  $58068

b. Future value of $58068 after 6 years = 58068*(1+0.065/12)^(12*6) = $85675.10

1 Figure 8.32 Annual Interest rate 8% Number of payments 5 Amount of payment -10 Present value 0 Payment at the end of period 0 Future Value $                                 58.67 Figure 8.33 Discounting factor of 12% at year 4 0.636 Present value of $3000 $                           1,908.00 Figure 8.34 annuity factor of 9% for 6 years 4.486 Annuity amount (5000/4.486) $                           1,114.58 Figure 8.35 Year DF @10% Cash Flow PV 0 1 1 0.909090909 100 90.91 2 0.826446281 50 41.32 3 0.751314801 100 75.13 4 0.683013455 50 34.15 5 0.620921323 100 62.09 303.61 Present value P $                               303.61

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