A loan is repayable over ten years by a special decreasing annuity, calculated on the
basis of an effective interest rate of 10% per annum. The annuity payment each year
is divided into an interest payment (equal to 10% of the loan outstanding at the start
of the year) and a capital payment, which is used to reduce the amount of the loan
The annuity decreases in such a way that, if income tax of 30% of the interest content
of each annuity payment were to be deducted from each payment, the net amount
of the payment (i.e the capital payment plus the interest payment less tax) would be
R5000 each year.
An investor who is not liable to tax will in fact receive the gross amount of each
annuity payment (i.e the payment without any deduction). What price should such an
investor pay for the annuity to achieve an effective yield of 8% per annum?