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

Question

Compute the unknown values for the four cash -flow diagrams shown. Your real estate taxes are S3, 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

1. Fig 8.32

F = P((1+i)^n - 1) /i here P is periodic payment, n = no of periods = 10((1.08)^5-1)/0.08 = $58.67

Fig 8.33

P = F/(1+i)^n = 3000/(1.12)^4 = $1906.55

Fig 8.34

A = (P*i*(1+i)^n) / ((1+i)^n-1) = 5000*0.09*1.09^6/(1.09^6-1) = $1114.6

Fig 8.35

P = 100/1+i + 50/(1+i)^2 + 100/(1+i)^3 + 50/(1+i)^4 + 100/(1+i)^5 = 100/1.1 + 50/1.21 + 100/1.331 + 50/1.4641 + 100/1.61051 = $303.61

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