Step-by-step explanation:
To solve this problem, we need to first calculate the present value of the 6 equal annual payments. We can use the formula for the present value of an annuity to do this:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of periods.
Using this formula with the given values, we get:
PV = 2500 * [(1 - (1 + 0.035)^-6) / 0.035] = 12,758.61
So the present value of the 6 equal annual payments is R12,758.61.
Next, we need to calculate the outstanding principal just after the 3rd periodic payment. To do this, we can use the formula for the future value of an annuity:
FV = PMT * [(1 + r)^n - 1 / r]
Where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of periods.
Using this formula with the given values, we get:
FV = 2500 * [(1 + 0.035)^3 - 1 / 0.035] = 8,989.11
So the outstanding principal just after the 3rd periodic payment is:
R10,000 - R8,989.11 = R1,010.89