Page 27 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes 2.3.1 Future Value of Annuity of 1

If you open a savings account that compounds interest each month, and at the end of each month
you deposit 100 in the savings account, your deposits are the rents of an annuity. After 1 year,
you will have 12 deposits of 100 each, and a total of 1200, but the account will have more than
1200 in it because each deposit earns interest. If the interest rate is 6 per cent a year, compounded
monthly, your balance is 1233.56. The future value of an annuity or amount of annuity is the
sum accumulated in the future from all the rents paid and the interest earned by the rents. The
abbreviation FV is used for the future value of an annuity to differentiate it from the lower case
fv used for the future value of 1.
To obtain a table of future values of annuities, we assume payments of 1 each period made into
a fund that earns 8 per cent interest compounded each period. The following diagram illustrates
an annuity of four payments of 1, each paid at the end of each period, with interest of 8 per cent
compounded each period.
8% interest per period

1 1 1 1

P 1 2 3 4 n FV

Time Periods

Notice that there are four rents and four periods, each rent is paid at the end of each period. At
the end of the first period, 1 is deposited and earns interest for three periods. The next rent
earns interest for two periods, and so on. The amount at the end of the fourth period can be
determined by calculating the future value of each individual 1 deposit as follows:

Future value of 1 at 8% for 3 periods = 1.25971
Future value of 1 at 8% for 2 periods = 1.16640
Future value of 1 at 8% for 1 period = 1.08000

The fourth rent of 1 earns no interest = 1.0000
Total for 4 rents 4.50611
The formula for the future value of an annuity of 1 can be used to produce tables for a variety
of periods and interest rates

Example: In the beginning of 2006, the directors of Molloy Corporation decided that
plant facilities will have to be expanded in a few years. The company plans to invest: 50,000
every year, starting on June 30, 2006, into a trust fund that earns 11 per cent interest compounded
annually. How much money will be in the fund on June 30, 2010, after the last deposit has been
made?
Solution: The first deposit is made at the end of the first 1-year period, and there is a total of 5
periods. The last deposit, made on June 30, 2010 earns no interest. The investment is an ordinary
annuity with n = 5 and i = 11 per cent. From Table Future Value of Annuity 1 we find that the
amount of an ordinary annuity of 1 is 6.22780.

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