Question

Calculate the future value of the following annuity streams:

a. $5,000 received each year for 6 years on the last day of each year if your investments pay 6 percent compounded annually.
b. $5,000 received each quarter for 6 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.
c. $5,000 received each year for 6 years on the first day of each year if your investments pay 6 percent compounded annually.
d. $5,000 received each quarter for 6 years on the first day of each quarter if your investments pay 6 percent compounded quarte

Answer 1

a. Amount received on last day of year = 5000, No of years = 6 , Rate = 6% compounded annually

This is an ordinary annuity with payments at the end of the period and to find the future value, we will use fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt)

Using fv function in excel, we get future value = 34876.59

b. Amount received on last day of quarter = 5000, No of years = 6 = 6 x 4 quarters = 24 quarters , Rate = 6% compounded quarterly

quarterly rate = Rate/ 4 = 6%/4 = 1.5%

This is an ordinary annuity with payments at the end of the period and to find the future value, we will use fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt)

Using fv function in excel, we get future value = 143167.60

c.

Amount received on first day of year = 5000, No of years = 6 , Rate = 6% compounded annually

This is an annuity due with payments at the beginning of the period and to find the future value, we will use fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt,-pv,type)

In this formula, we take type=1 as payments are received at the beginning of the period and pv=0 because as there is no initial lump sump received

Using fv function in excel, we get future value of annuity = 36969.19

d Amount received on first day of quarter = 5000, No of years = 6 = 6 x 4 quarters = 24 quarters , Rate = 6% compounded quarterly

quarterly rate = Rate/ 4 = 6%/4 = 1.5%

This is an annuity due with payments at the beginning of the period and to find the future value, we will use fv function in excel

Formula to be used in excel: =fv(rate,nper,-pmt,-pv,type)

In this formula, we take type=1 as payments are received at the beginning of the period and pv=0 because there is no initial lump sump received

Using fv function in excel, we get future value = 145315.12