Annuities and Sinking Funds

1
Annuities and Sinking Funds

• 12.4.1

2
Annuity

• Ordinary annuity a fixed (or escalating )
  investment usually every month for a certain
  fixed period often until the age of 65yrs,
• FV Future Value
• FV ( Ordinary) the amount is invested at the
  end of each month.
• FV (Annuity due) the amount is invested at
  the beginning of each month receive more
  interest.
• Tax Deferred Annuity deducted at source until
  retirement. Tax is calculated after the
  deduction, resulting in tax savings

3
Sinking Funds

• This is an annuity that is invested for a
  specific purpose and is continued for a
  predefined period.
• Examples
• Childs college fund
• To buy a new computer in 3 years time.

4

• It is estimated that you will need R 600 000
  for your childs education in 10 years time, How
  much must you put away each year if you receive
  10 interest pa.

5
FV (ordinary annuity )
FV 600 000 I 10/100 0.1 n 10 yrs
R 37 647.48
6

• How much would you need to invest each month to
  receive the same amount?

12
R 2 929.04
R2929.04 X 12 R35148.53 Pay
R2498.95 less pa or R 24 989.50
over 10 yrs
7
FV ( annuity due) FV (ordinary annuity) x
Save using annuity due
X
If we worked out the same problem using annuity
due formula.
8
FV ( annuity due)
X
X
600 000
R 34 224.76
9
Bond Repayments

• To work out monthly bond repayments, the
  following formula is used.

Im is the monthly instalments CP cost price of
the house etc i rate of interest r/100 n
number of repayments
10
As this formula contains negative exponents , it
may be re-arranged to give ..
11
Bond Repayments

• To work out monthly bond repayments, the
  following formula is used.

Im is the monthly instalments CP cost price of
the house etc i rate of interest r/100 n
number of repayments
12
Bond Repayments
Work out the monthly bond repayment (instalment)
on a R 500 000 house over 20 years at a mortgage
rate of 12 pa.
i (12/100) /12 0,01 n 20 x 12 240
R 5505.43