How much must be invested today if you want to receive R15000 at the beginning of every quarter for the next 11 years from a financial institution that offers 9% effective interest per annum compounded quarterly.?
To calculate the amount that must be invested today, we can use the formula for the present value of an annuity with compound interest:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value (amount to be invested today)
PMT = Payment per quarter (R15000)
r = Quarterly interest rate (9% / 4 = 0.09 / 4 = 0.0225)
n = Number of quarters (11 years * 4 quarters per year = 44 quarters)
Plugging in the values:
PV = R15000 * [1 - (1 + 0.0225)^-44] / 0.0225
PV = R15000 * [1 - (1.0225)^-44] / 0.0225
PV = R15000 * [1 - 0.5490] / 0.0225
PV = R15000 * 0.4510 / 0.0225
PV = R15000 * 20.0444
PV = R300,666.67
Therefore, you must invest R300,666.67 today in order to receive R15000 at the beginning of every quarter for the next 11 years from a financial institution offering 9% effective interest per annum compounded quarterly.