Question

Calculate the future value of the following annuity streams:

a. $5,000 received each year for five years on the last day of each year if your investments pay 6 percent compounded annually.

b. $5,000 received each quarter for five years on the last day of each quarter if your investments pay 6 percent compounded quarterly.

c. $5,000 received each year for five years on the first day of each year if your investments pay 6 percent compounded annually.

d. $5,000 received each quarter for five years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

Answer 1

(a) Annuity Value = $ 5000, Annuity Tenure = 5 years, Annuity Frequency: Annual, Interest Rate = 6%, Compounding Frequency:Annual

Applicable Interest Rate = Annual Interest Rate / Compounding Frequency per Annum = 6 / 1 = 6%

Total Future Value = 5000 x (1.06)^(4) +.............+ 5000 = 5000 x [{(1.06)^(5)-1}/{1.06-1}] = $ 28185.46

(b)

Annuity Value = $ 5000, Annuity Tenure = 5 years or (5x4) = 20 quarters, Annuity Frequency: quarterly, Interest Rate = 6%, Compounding Frequency:quarterly

Applicable Interest Rate = Annual Interest Rate / Compounding Frequency per Annum = 6 / 4 = 1.5%

Total Future Value = 5000 x (1.015)^(19) +.............+ 5000 = 5000 x [{(1.015)^(20)-1}/{1.015-1}] = $ 115618.33

(c) Payments received at the beginning of the period are example of annuity due. In this scenario, the payments are compounded for one additional period as compared to ordinary annuities. Hence, the future value would also be greater than the future value of an ordinary annuity by one additional compounding.

Future Value = 28185.46 x (1.06) = $29876.59

(d) Payments received at the beginning of the period are example of annuity due. In this scenario, the payments are compounded for one additional period as compared to ordinary annuities. Hence, the future value would also be greater than the future value of an ordinary annuity by one additional compounding.

Future Value = 115618.33 x (1.015) = $ 117352.61