Ques. 1) Your uncle promises to give you $550 per quarter for the next five year

Question

Ques. 1) Your uncle promises to give you $550 per quarter for the next five years starting today. How much is his promise worth right now if the interest rate is 8% compounded quarterly?


Ques. 2) Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

a. The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
b. The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
d. The periodic rate of interest is 3% and the effective rate of interest is 6%.
e. The periodic rate of interest is 6% and the effective rate of interest is also 6%.

Explanation / Answer

Ques. 1) Your uncle promises to give you $550 per quarter for the next five years starting today. How much is his promise worth right now if the interest rate is 8% compounded quarterly? Here we have to find PV of AnnuityDue= PVAn (Annuity due) = PMT(PVIFAi,n)(1+ i) We have PMT = $500, i=8%/4 = 2% (Qtrly compounding) n = time period = 5years*4 Qtr/year = 20 So PVAn = (1+i)* PMT*(1/i - 1/(i(1+i)^n)) So we get PVAn = (1+2%)*500*(1/2% -1/(2%*(1+2%)^20)) ie PVAn = 510*(50-33.65) =510*16.35 = $8,338.50 So Uncle's promise is worth $8338.50 now. Ques. 2) Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.

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