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in BUS 2016H - Financial Mathematics by
 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?

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