Question

(1) What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually? 0 year =$0,1year =$100, 2year= $100, 3year = $100

(2) What is the PV of the same stream?

(3) Is the stream an annuity?

(4) An important rule is that you should never show a simple rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when rSIMPLE = rEAR = rPER.) What would be wrong with your answer to parts (1) and (2) if you used the simple rate 10%rather than the periodic rate rSIMPLE/2 = 10%/2 = 5%?

Answer 1

Quoted interest rate is 10%, compounded semiannually, So effective annual rate is calculated below:

Effective annual rate = [(1 + 10% /2) ^ 2] - 1

= 1.1025 - 1

= 10.25%

Effective annual rate is 10.25%.

a.

Future value = [$100 × (1 + 10.25%) ^ 2] + [$100 × (1 + 10.25%) ^ 1] + [$100 × (1 + 10.25%) ^ 0]

= ($100 × 1.2155) + ($100 × 1.1025) + ($100 × 1)

= $121.55 + $110.25 + $100

= $331.80.

Future value is $331.80.

b.

Present value = [$100 / (1 + 10.25%) ^ 1] + [$100 / (1 + 10.25%) ^ 2] + [$100 / (1 + 10.25%) ^ 3]

= ($100 / 1.1025) + ($100 / 1.2155) + ($100 / 1.3401)

= $90.70 + $82.27 + $74.62

= $247.59

Present value is $247.59.

c.

SInce,the cash flow has equal payment at end of each year for 3 year. So,the cash flow stream is an annuity.

d.

Quoted interest rate is 10%, compounded semiannually, it mean the interest is compounded twice in a year. if we use simple 10% interest rate then semiannual compounding (interest on interest)is not consider in calculation. So, in this the future value and present value calculation would be wrong.