Question

What is the present value of the following annuity? $3,926 every quarter year at the end of the quarter for the next 7 years, discounted back to the present at 12.58 percent per year, compounded annually?

You are given an investment to analyze. The cash flows from this investment are

End of year

1.1,695

2. 5,810

3. 982

4. 1,613

5.1,063

What is the future value of this investment at the end of year five if 10.55 percent per year is the appropriate interest (discount) rate?

Answer 1

1). APR(compounding quarterly) = m * [(1 + EAR)^1/m - 1]; m = no. of compounded periods in a year

= 4 * [(1 + 0.1258)^1/4 - 1]

= 4 * [1.0301 - 1] = 4 * 0.0301 = 0.1203, or 12.03%

PV of Annuity = Quarterly Payment * [{1 - (1 + r)^-n} / r]

= $3,926 * [{1 - (1 + 0.1203/4)^-(7*4)} / (0.1203/4)]

= $3,926 * [0.5637 / 0.0301]

= $3,926 * 18.7488 = $73,607.96

2). FV = [CF(i) * (1 + r)^(n-i)]

= [1,695*(1+0.1055)^(5-1)] + [5,810*(1+0.1055)^(5-2)] + [982*(1+0.1055)^(5-3)] + [1,613*(1+0.1055)^(5-4)] + [1,063*(1+0.1055)^(5-5)]

= 2,531.66 + 7,849.69 + 1,200.13 + 1,783.17 + 1,063 = 14,427.65